Of course, I stil disagree with you.
The difference between your original scenario and what I described is that there was a force involved in my sitch.
You describe R1 rounding second and coming to third. The moment he touched second baes, he legally acquired it. If he decides to advance to third, preceding runners are not forced to advance. R2 doesn't have to give up his place on third. R3 was already forced to move earlier in the play, so he's in the wrong spot. So R1 and R3 are out if all three are tagged on the base.
In order for R2 to be out, R1 would have to be tagged prior to reaching second, thus removing the force. Once he passes second, the force is off.