Hey, Ev
I’ve been through your dilemma — I shot and loved the 200-500 5.6 and now shoot the 180-600, the 400 4.5, and the 400 2.8TC.
Honestly, as JA notes, the 180-600mm is an excellent direct replacement for your 200-500mm.
I agree with you on the loss of a 1/3 stop — f/6.3 is slow for low light situations.
But the 180-600 also gives you 100mm more reach, so you’ll be enlarging your noise less at any given distance.
Sharpness is superior to the 200-500 and the zoom is internal, and it’s 3/4 of a lb lighter than the 200-500.
It also takes a 1.4TC much better than the 200-500 for times when you simply must extend.
The only deficit I’ve noted is that it tends to throw a bit more chroma than the 200-500 in bright high contrast situations (e.g. a fast white seagull on a very bright blue sky).
Another alternative is the 400 4.5 — it’s optically superb, rivalling the 400 2.8 for 1/5 of the price.
It’s feather light (2.5lbs), and handles a TC really well to become a high quality 560mm 6.3,
(The sharpness of my 400 4.5 +TC matches the sharpness of the 180-600 naked and significantly exceeds the 200-500).
The extra light gathering is significant in blue hour, and you can add the TC when the day gets brighter.
Tiny birds that refuse to let you get close will be challenging but, if you can get close, the results you get will be superb.
I haven’t shot the 100-400 5.6, but it gets lots of praise.
Remember you’ll have to crop more with it and that means enlarging noise.
But it’s pretty light and will take a TC better than your 200-500.
Needless to say, the 400 2.8 TC is the pinnacle for low light — f/2.8 and it becomes a beautiful 560 f/4 with a flip of a lever.
Performance with the TC is outstanding.
Shooting with it is transformational. I’m able to get blue hour shots that would be otherwise impossible.
The weight’s nothing to sneeze at 6.5 lbs — a pound and a half extra over your 200-500.
Still, I shoot it handheld all day. Your mileage may vary.
But, of course, there’s the price — yikes.
Finally, the 70-200mm f/2.8 with a 2xTC will get the job done, but I don’t recommend it for your case.
The 180-600 gives you 200mm more reach so you won’t be cropping and enlarging noise.
After shooting the 200-500, I think you’d find the 70-200 frustrating for small subjects.
Good luck!