Maybe it is more your technique than the tool, or maybe not.
I dont now if a better tool is the answer, but I will relate a bit of my own ON-topic experience.
If you can justify the cost of buying a better tool, BUY THE TOOL.
I dont know what file you have, I have the cheapy Dobco red one (large), I couldnt find the Medium/Orange handle one at the time.
I dont have any vintage small fret guitars (yet), so it works fine.
IF I recall, you have the z-shaped one with wood bulb shaped handle and the file inserts that go on the end. That is reported to be a pretty good tool.
I only take maybe 4-6 firm but fairly light strokes canted slightly left, then same canted slight right , then one or two light pressure passes perpendicular. I do this following the radius of the fret, so only a portion of the length of the fret is having material moved during those passes.
That gets me very close all but what were the highest frets, which would have be the most flat-filed.
These are on the typical nickel blend fret; stainless would be more work I am told.
Looking closely at that thin crown line will tell you what needs more attention, be it center, treble or bass side; often it is one end or the other and not the whole fret that was high(er) than the imagined infinite tangential planes along the radius and length of the fret board; like if there were an infinite number of strings.
I dont experience that type of fatigue or pain at all. My fingers do get a little tired during the process but not anything like you describe. My hands have done a lot of physical type tool in hand jobs over the decades, so I dont know how that would factor in comparing.
How much should it take to file the 2 sharp edged shoulders created when leveling back to a crown?
If you are going past that and take anything off the dead center (the crown itself) you have lost the leveling.
I'm not saying that is what you are doing, just something to consider.
Long story, but it gives you something to compare how much filing we each may be doing.
Short answer, will it solve this problem? I dont know.
Should you buy the tool if you can justify the cost? HELL YES.