FWIW: MIL-PRF-5606 and MIL-PRF-83282 are considered compatible. The main difference is 83282 is limited on the cold side and not as popular in GA so not all FBOs may have it if you need it. That's one reason some people don't switch over. To the best of my knowledge Cessna and Piper do not offer any guidance on switching to 83282. But there are other acceptable guidance sources that allow it. Here are a couple, but for some reason I couldn't get any links to work.
AC 43.13-1B, Para. 9-27(b):
"MIL-H-83282 is significantly more flame resistant than MIL-H-5606, but a disadvantage is the high viscosity at low temperature. It is generally limited to -40 �F. However, it can be used in the same system and with the same seals, gaskets, and hoses as MIL-H-5606."
Cleveland Technicians Service Guide, AWBTSG0001-21, Page 21:
"Hydraulic Applications - Use fluids compatible with the systemMIL-H-5606 / MIL-H-83282 (Red Oils)"
There were also several ADs issued for various reasons which required the change from 5606 to 83282 and per the AD it was a simple flush of the 5606 and re-service with 83282 fluid. It was through a helicopter AD that I learned of the compatibility. Considering an AD is "approved" data that pretty much backs up the above acceptable guidance. However, I only helped 2 people convert to 83282 in their aircraft as 83282 wasn't readily available unless they carried a can or two on board. Most didn't consider the fire danger issue enough to convert from 5606 on their little puddle jumpers.