[greymule]

In the OP, the only possible reason the runner could be returning to 2B is that he failed to touch it and figures the defense will appeal. I would consider the tag out an obvious appeal play (like a runner obviously off a base when a line drive is caught by an infielder) and nullify the run.

Otherwise, even after the runner was put out for the third out, I would allow the appeal on the advantageous 4th out as Steve says.

The statement in the OP, "R1 never legally advanced to 2B," is wrong.

I'm not going to dig out my J/R, but I can't believe the J/R would not allow the advantageous appeal. I suspect the OP is being confused with that play where the sliding (forced) runner misses 2B but passes it and is then tagged out reaching back for the bag.