Yes, you have it about right, but to be precise I want to reword it slightly, with my edits in italics.
1. For the same generation and technology of sensor, pixel density has no bearing on ISO/noise performance
I add a hedge only because for all I know, two sensors designed on the same day could be slightly modified to favor one spec over another. A little noise might be traded off for some other feature deemed important. In technical life and physics, there are so few free lunches that often one feature must be balanced against another.
Perhaps a little noise can be traded off for more bandwidth? That seems reasonable to me, not being a sensor engineer but understanding some things about larger scale electronic designs and the associated juggling of compromises.
This is very true for lenses where, for example, something like sharpness in corners might be traded for chromatic abberation, or a feature like internal focusing tends to create certain undesirable behavior such as CA. Bjorn Rorslett makes a big deal about the "evils" of IF design on his old site.
I am stressing this because I am not cuttting decimal places when I look at various comparative test results, yet you certainly are. From my perspective, taking what I believe to be a realistic view toward the entire testing process, for all intents and purposes sensors made in the same era are remarkably similar (in my opinion) regardless of density (including D800). You can argue that forever if you look too closely. More on that later.
2. Relying on DX to replace a 1.4x tele extender is folly Particularly in situations whereif noise is going to be an overriding factor.
I'll talk about your HDTV lighting later.
3. Noise performance can only be bettered by increasing the light gathering power of the front element and/or increasing the sensor size. Corollary here is that my 300/2.8 should do SIGNIFICANTLY better than my 70-200/2.8 because the aperture focal ratio isn't a factor, merely the size of the front element. And in this case, it's more than twice the area.
In the case where your distance is fixed (sports in particular,of course) and 200mm is not enough, then 300/2.8 (bigger front element) is far preferable than 200/2.8 + 1.4x TC, regardless of sensor. F/2.8 is simply better than f/4, but if you can fill the frame by modifying your distance then f/2.8 is f/2.8 regardless of focal length.
I know... duh.... but I had to add that for clarity.
Bigger front elements gather more light on the front end. Bigger sensors gather more light on the back end. Make both as big as possible and you have a dynamic duo.
When you get into discussions of light gathering power we have to be very careful about terminology. In casual photographic discussion "aperture" (a linear dimension) is used interchangeably with focal ratio (a ratio of two numbers).
This works in practice because the concept of light gathering power is off the radar screens of most photographers. They generally have a fuzzy idea that those big front elements do something, and somehow are needed for long fast glass, but they generally do not think in the terms I have expressed here.
If you get a dozen amateur (or pro) astronomers together for a discussion they will always use "aperture" as a linear diameter of their lens front element. They talk about their 5" aperture lens (similar to a 500/4 in size). They will always specify focal ratio correctly, or as "f/" in shorthand. To do any other would turn the discussions into nonsense and no one would be sure what the other guys are actually trying to say.
Astronomers, in general, are obsessed with light gathering power (LGP). Focal ratio is important but it can be pushed and pulled with add-on optics. They live and breath this concept that all that matters is the size of the glass.
Astronomers can never change their working distances . With the exception of a few Apollo astronauts that got nice images of the moon with relatively short lenses. Those that are reach impaired and cannot change their working distances bow down to the god of LGP. Some just do not know they are doing so
When you used "aperture" above in #3, I assume you meant focal ratio.
A thought about light transmission performance improvements. In short, Wikipedia, for example, suggests lens surfaces scatter only 0.3% of the light that hits them. Even an 11 element design like the 300/2.8 should pass 96+% of the light. It is impossible to get to 100% so you can safely assume there are negligible gains to be made.
The citation for that number is an online Hoya filter marketing slick. I hope it is real and not a figment of their ad department's imagination but it is more or less in line with numbers I've seen over the years. It's just a non-issue in real life so it is hard to google precise numbers, for example.
A little bit of scattered lost light can create noticeable flare and that is why lens makers often make great hay by increasing their light transmission by 0.1%. Plus, they are practicing a 400 year old craft and there is simply little blood left in that stone to squeeze, and they need to fill their marketing slicks with something.
There is a difference between light transmission loss causing a lens to perform less than spec, verse simply "lying" or "fibbing" a bit. My 35/1.4 Ai is a classic example, where it is, in truth, an f/1.8 lens and that is obvious in simple tests. It is infamous for this, and I suspect there is more fibbing than light loss involved. It's not like the lens has 30 elements in it.
Consider the 70-200 with 21 pieces of glass. As far as I know, my V1 lens is reasonably close to true f/2.8 but I have not seriously looked at that since 2004 when I bought it. If light loss were an issue that lens would be a true t/4 by the time any light leaked out the back end
Now your Pros shooting in HDTV light. Here is my analysis, dovetailing everything I have said into that situation, which could not be more different than your night soccer candle light game...
1. The lighting is such that they are guaranteed 1/800s at ISO 1600.
2. They are shooting a D3s or now D4. If they are reasonably filling the frame with big glass then the D3s is delivering stellar pictures and really just loafing along at ISO 1600.
3. They could presumably deliver ISO 3200 to their editors/clients/employers and it would be acceptable if the reason made sense. Just because the D3s is so good.
4. Now they want a DX camera and lighter lens and, in effect, they are willing to drop that stop and deliver images comparable to the D3s at ISO 3200, and that will be acceptable.
That's the best I can piece it together. You were not clear what cameras they would do this with, etc., nor the exact circumstances, and the detail may be beyond the scope of what we want to get into. But that is effectively what they will get if they do that, and if they think otherwise they are either kidding themselves or defying physics. Or found a camera virtually identical to Bill Claff's ideal performance.
Now, D3s vs D4. DXO says the D3s edges out the D4, by an amount you acknowledge is insignificant and not noticeable in real life but you are curious about all things.
Bill Claff's numbers suggest the opposite. The D4 edges out the D3 at moderate to high ISO's, in a similarly inconsequential amount.
We could bring Bill into the discssion to sort out that 0.2 stops or whatever it is. But here is my advice on how I personally look at these things...
Just because a tester commits a number to paper does not make it The Gospel Ultimate Truth, expecially when there is great precision involved in the number. There are potential observational or procedural errors. There is potential sample variation. Has anyone ever taken a dozen same model Nikon's and subjected them to these tests?
And finally, Bill and DXO may not be measuring exactly the same thing, to the extent that they would be expected to agree to within 0.1 stop even if every other aspect of their test is impeccable.
So when I see small inconsistencies like that, I chalk it off to "expected measuring error" and assume the two cameras are identical. Even if Bill and DXO agree on two cameras, and they are similarly close, I assume the cameras are identical within measurable error.
You are free to disagree with my way of thinking there, but then at a minimum I think you need to get all details of the tests, and in particular all the source code for the programs they used for their tests and study them, line by line, to ensure they are really doing the same things. Good luck . After all, these results are spit out by computers.
Short story: don't look too closely. Best advice I can give you.
As to DXO's tests, do you know exactly what they mean by "suffer perceptibly"? Would you know a noise level of precisely 30 db (and not 31db) if you saw it? The D4 is rated at ISO 2954. What does it look like at ISO 1600 or ISO 3200?
If the noise lines were ruler straight, from one end to the other, then one number could be reasonably extrapolated to other numbers if you fully understand the underlying math.
But in reality, at least according to Bills more fine grained charts, the lines wander around quite a bit and do some things I surely don't understand.
If Bill's wandering lines are remotely correct then one number absolutely, positively, cannot say it all and needs to be taken with two or three grains of salt.
Personally I do not trust the usefulness of a single number. It makes for easy rankings (I see you look at that aspect closely). I think it is unwise to place too much stock in a complex test such as noise performance, reduced to a single number. Again, you are free to disagree.
I don't blame DXo for this. I blame humanity's universal desire to boil down complex issues into one number or something similarly over-simplified.
But when I look at all these numbers, I must come to the conclusion that sensor density has no direct bearing on noise level. And for the most part, within a reasonable time frame all else is remarkably equal if you don't cut too many decimal places when interpreting the results. I've explained how I interpret these things as best I can.
And interestingly, quite the opposite although not in the context of your shooting problems.
At the low end of the ISO range, the D800 absolutely, positively destroys every other camera in terms of sheer dynamic range. Although not terribly relevant to your basic shooting problems, I think that is something that needs more thought and research. Why???? Maybe a few more ultra-high resolution camera models are needed in order to determine if there is a pattern and trend.