I am still not doing birding or BIF at all, but i am willing to start this in my rest of life later, i only depends in cameras i use for sports so it is the same to be used for birding, 1DX was and still my workhorse until now, i know people used to use even slower camera than this in long time ago in the past such as D2 from Nikon or 1D mk1 and 1D2 and 20D and 30D and 7Dmk1, so whatever camera i upgrade to it will definitely do the job, but i have to choose which one rather than getting 2-3 and sell one later.
As for lenses, i was thinking that will be Phase/Stage 2 after buying the camera body, for now i have 70-200 mk2 as my latest lens i bought, it is still holding its performance strong, while for my vintage 300 2.8 mk1 it is time for new one, i don't know if i can go to something like 500-600 lenses, but i can get a zoom lens for that 500-600mm end, and i saw some new zoom models that are nice enough and can be affordable more over excellent primes, i dreamed in the past about 400mm f2.8 and 600mm f4, now the dream is gone forever, even if i sell my house i don't think i have to run to buy 400 and 600 and leave them for dust, also if i can make staged photography of birds then i can use manual optics, i have telescopes that can go to any focal length, even 2700mm, i have two telescopes that can be used like lenses, one with 540mm focal length and the other is 700mm native [f6 and f6.6], for birds in still they can be used, speed isn't important, only BIF i need AF magic, and i used manual through years with experience, with practice on some spots i can manage manual focus, my garden has a lot of trees brunches i can focus on, and with f6-f8 it will give enough DOF and BG isolation.
