But I think it's an important clue as to what's happening, PITA or not.
I've opted for resetting the flow rate once the valve has warmed up. Since that works, I don't really see how it could be an impediment in the line or anything but a bad valve or washer.
I would pull it and replace the washer, which is on my list of things to do. My issues started after I replaced an old washer. It's also possible that there's an impediment in the pipe that expands when warm. I once extracted an acorn(!) from behind the kitchen faucet aerator after I noticed an intermittent rise and fall of the flow rate. As it rotated around in the faucet arm, it varied the flow (it was not perfectly round). FWIW, I installed a water filter right after that incident. (-: But I don't think that's your problem.
Since the slop sink valves are usually located at one of the lowest points in the whole piping system, garbage in the lines could easily find its way down there. I'm still of the mind that it's the faucet washer. Was it flat or conical?
Since it doesn't exhibit the problem at maximum flow, it does seem to me to be the valve washer. Although the initial valve setting allows a slow flow, once the washer and seat heat up, that small gap narrows and the flow slows. On my sink, the flow will go from perhaps a half gallon per minute to a very slow trickle - just a few drops.
Good luck. I haven't fixed it because it keeps me from wasting the hot water accidentally. (-: It's like having a faucet ghost saying "you didn't mean to leave the hot water running full blast, did you?" Of course, I have managed to leave it trickling hot water when I though the valve was closed.
-- Bobby G.