My experience with this is the crash occurs when I attempt to use the stamina that I had before the spillover:

Had 250 stam before leveling, spillover raised the total to 642/392. I didn't use any raid points or gathering after leveling, just continued running whaleship and was able to do this 8 times; the moment I tried running another mission with 242/392, FKG crashed. But when I loaded it back up, I was still at 242/392 and was able to continue running whaleship as normal. After I ran out of stam, then I used my gathering points.

My advice is not to burn your raid points/gather points until after FKG crashes and see if it affects your stam still. It'll be awhile before I level again, but I'll try to remember to record it if the bug is still happening then.