I sold all my Canons except one. I kept my 1D Mark III & 300 F4L & 150-600. Strictly for birding from my kayak.
I got rid of two 5D's, 1Ds Mark II, and several L's, including the 135L, and all my primes, etc, and moved to Fuji.
I use the Fuji X-T1 daily.
I do not miss the full frames from Canon.
Fuji has a very good 400m lens now. You could sell your remaining Canon stuff and strictly use Fuji. The X-T1 has great focus and 8 FPS and it's really good at it and the new 400mm from Fuji is wicked sharp. People bird with that setup. You could sell your remaining Canon stuff and go to that lens and be done with having two systems to support.
Also, depending on what you're shooting, you could just adapt your Sigma telephoto to Fuji mount, and use focus peaking and still have 8 FPS. Focus peaking makes focus trivial.
I shoot with a Fuji X-T1 & Fuji X100S 99% these days.
The only reason I kept my 1D Mark III is because they're $400 cameras, worthless to sell, and is something I don't care about when I'm in my kayak on the water. I frankly don't use it much. I don't miss it either when I'm shooting Fuji.
I don't miss my full frames at all. I have 12mm F2, 21mm F1.4, 50mm F1.2 and 85mm F1.4. The "look" I liked from my full frame Canons show up very similar with these lenses, with a much smaller, more easy to use, no missed focus kit. Love it. And with the X100S, it has a built in 23mm F2 pancake. It's simply a joy to use when out and about and dead silent. I can't mention enough how much I love the silence of these cameras (I use electronic shutter when there's not a ton of action going on or when I'm not using lighting).
The only thing I haven't added yet is a 35mm F0.95 that I'm eyeballing.
If you want a beater Canon for twice a year with a telephoto and sparse use, I'd get a used 7D or 1D3. They're $400 or less. So it's not like you have a $800+ camera sitting on a shelf for 4~5 months at a time. And they're built like tanks and take a beating. While there are clearly better cameras available, why spend twice as much for some day light application sports twice a year?