HI Tritium, I hope your ID doesn't indicate what you mess with for a hobby. You haven't said whether the keys are rectangular or Woodruff, and you haven't said whether you have access to a milling machine. If they are rectangular keys, the usual fix is to mill another keyway in the shaft, 90 degrees around from the original one, then fit a key identical to the original one. That gets you back to having a fully repairable machine that uses standard parts. If you can source replacement sprockets, there is no drama relating to the job except for cutting the keyway, which is easy (as milling jobs go - you do need careful setting up, and a saw or endmill of exactly the right width to match a standard key).
Normally I would not expect a combination of a grubscrew and a loose key to work any better than a loose key by itself: in other words, not at all. I also think your plan to precision-grind the width of a welded-in key, in place, is impractical. You could probably deal with the height that way, but not the width.
So far as the wheels are concerned, the best solution is to get another pair. Short of that, depending on their design you may be able to either bore and sleeve the ones you have, or cut the centers out of the wheels, make new steel hubs, and bolt the new hubs to the old wheels.
