I think you need to take a problem solving/process of elimination approach. Do whatever makes sensible order, considering inconvenience and/or time.
1. You are shooting from inside a home, presumably around 65-72F ambient to outside more like 30 degrees ambient. That is a 40 degree difference and that can easily result in a mirage effect. Shoot outside and give your lens an hour to cool down before shooting. Once cooled down leave it outside if possible until all tests are done for the day.
This is actually at the top of my likely list of suspects, and the easiest for you to test.
2. I would shoot something on a 45d angle and post it here. Two things to test... 1) Doesn't matter where you focus; you want to see if *something* is in focus. If something is in focus then you need to figure out where it's focusing. As Jim says, DOF at 25' is quite thin although that is about where you can expect the sharpest images, strictly based on image quality and without regard for focus accuracy.
3. In your profile you list an "RRS SB55". I assume you mean a BH-55 head. If you have that head, swap it in, but use the long lens support (can't hurt). Eliminate the gimbal. I have never shot that gimbal so I have no opinion of it. I would like to try one out some day.
Just for your sanity, never look to RRS to tell you that their gear might or might not be quite up to snuff for any given application. I've had that conversation (regarding that Long Lens Support). Trust me on that one.
4. If you shoot hands off, in Mup mode, with a MINIMUM 5 second delay you will get the sharpest image possible, assuming no wind. Which may be tough this time of year but this stuff is never easy. The slightest puff of wind will nullify that test (especially on a Series 3). I actually test my 500/4 indoors solely because of this problem, even though the working space is difficult to deal with.
5. If you can, try a Series 5. You don't want to buy another tripod but the lens does not care what you think or want:-). The Series 3 is marginal, to the extent that it takes more skill and daring than a Series 5. I get about 50-70% consistency on a Series 3 with a 500/4 working 700-850mm.
But I didn't buy the lens last week for a trip across country next week. It takes time to perfect the technique - more like months or years, not days. A Series 5 would likely speed that up. Your decision there.
6. That image was with VR off. You might want to try VR on to find if all those guys that dumped their AFS lenses for the VR model knew what they were doing. I have no firm opinion, my 500 is AFS, not VR. It's a tool in your box, try it.
7. I would NOT shoot hands on with exposure delay. I mean literally *I*. Whenever I have done that, or shot with Mup by accident that way my timing is thrown off. Perhaps it is because I just don't shoot that way and not accustomed to the delay.
I have some reason to believe that exposure delay mode does not accomplish anything when using hands on Long Lens Technique. Rather than argue out the details I'm just suggesting that as part of your process of elimination try standard S mode when hands on, and a long Mup when hands off with a remote. You need to spend the time, experimenting with different techniques, to see what works for *you*.
8. If you want to take a 1.5- 2 hr drive, send me an email or PM. I'd be happy to meet up with you at a local nature park to check things out as best I can. You can also try my 500/4 and Wimberly on my Series 3, and we can trade results. That might help separate potential gear trouble from technique. We would need to pick a low wind day; I'm fairly flexible. You should be comfortable eliminating focus or optical issues before we do that.