A posting in another forum was by a gentleman with a problem that might be similar to your sharpening of arch punches.
He loaned out his grinding wheels and was unable to sharpen several large diameter drills when needed.
This gentleman stated that he had learned to sharpen drills on grinding wheels from several old pros, and he had become skilled in doing so.
Without having his grinder, he tried his belt sander and it did an even better and easier job than grinding wheels, especially in sharpening drills of over 1/4" diameter.
I'm guessing that many of your arch punches are over 1/4" and maybe a belt sander is an efficient way of sharpening them.