If you're really lucky, you might find new handles for that, but IMHO, it's doubtful. If the handles physically are in good shape, you might have the option of taking them to a metal restorer, and they could clean and plate them. That could get costly. While you can maintain that type of valve, it's illegal to install a new one, so that's one reason why it's hard to find anything. If you find something, it would be old stock for something that hasn't been available new for many years. Code today requires anti-scald technology, and that valve does not have it.
If you were to try to change that out to a single handle one, you'd need to tear up a bunch of tile since there must be some distance from the valve to the tub spout, and you do not have it. If there was more room between the valve and the spout, a remodel plate could replace the valve with a new one in any finish you might want. I might be wrong about how much room you could gain with a remodel plate, but it would be close.