Depending on your local inspector's interpretation, anything other than maintenance to that existing ancient valve may dictate replacing it with one that meets current codes - that would be either a pressure balance or thermostatic anti-scald one. Most of those are single handle fixtures. They do make remodel plates that may be able to cover the old openings. You would need to build a box around the center where that stud is since (unless you wanted the valve offset), it would have to go right where the stud is now. That could get tricky keeping from damaging the tile, but it could be done.
YOu might try a different supply house, you might get lucky finding a stem that would work. Handles, on the other hand, might be harder...generic ones are often a poor fit and could strip out the new stems.