That is a really nice set. Too bad he didn't post the model # in his otherwise nicely written ad. 1928 was right about when the superhet was first introduced, by RCA of course, and nobody else got to use it for a couple years (RCA was the 400 lb gorilla and acted like it).
I have a similar set from Grebe, the Synchrophase, earlier and not superhet but the same type of speaker/table/base with radio on top.
I would not touch that finish, it looks fine to me for its age. And it's probably lacquer not varnish, with toned lacquers in some areas, so it's not that easy to reproduce if you strip it off.
Unfortunately he didn't post an asking price. $200 would be a bargain, market value probably more like $400 but it's so spotty with radios.