Small birds just need a long focal length. The 70-200 is a good lens, but nothing will make it a lens of choice for small birds. I'd consider the lens with a teleconverter better for large mammals or large wading birds - not small birds.
The other challenge you run into with cropping is the backgrounds are not smooth enough. A longer lens provides better subject isolation and smoother backgrounds.
Take a look at lenses like the Sigma 50-500 or 150-500 as good compromises. I have a Tamron 200-500 which is quite good at close range.
As mentioned above, you need good light. 1/1000 sec and ISO 200 would be the starting point. As you move to higher ISO levels, you increase noise but you also lose contrast and detail.
Also take a look at your post processing. Sharpening, contrast, and saturation can all add pixelation - especially on a cropped image. In some situations you can crop and then resize to a larger image size at the start of editing to reduce pixelation. You can also apply noise reduction selectively to the background.