Make the call -

[ManInBlue]

Originally Posted by Durham

NCAA rule 7-11 page 87.

f. The batter intentionally or unintentionally interferes with the catcher’s
fielding or throwing by stepping out of the batter’s box or making any
other movement that hinders a defensive player’s action at home plate;
PENALTY for f.—The runner(s) return to the base occupied at the time
of interference.
Exceptions—
(1) If the runner is advancing to home plate and there are fewer than two
outs, the runner, instead of the batter, is out.
(2) The batter is not out if any runner attempting to advance is put out,
or if the runner trying to score is called out for batter’s interference.
(3) If the batter also should strike out on the play, it is a double play.
(4) If a batter/runner and a catcher fielding the ball make contact, no call
shall be made unless either player attempts to alter the play.

Look at exception (1)

Look at exception 4 - in my scenario, one of the players is attempting to alter the play. So who's out in #4?

Look at that would ya, it's not such a TWP afterall. They wrote it in a rule book!!

Let's go with your answer for now (still clarifying the whole thing) - if R3 is advancing, you say he's out, put the batter back in the box. Does the pitch count?

No for a "yeah-but" - these are batter's interference, and the batter is actually now a runner. Do the BI rules still apply?