I'm not piling on, I admire someone who is willing to stick to their understanding of the rules and not be swayed... but, there was a wrong committed by the defense that should be awarded to the offense.
You say you would protect him to 3B, but the runner made it to 3B regardless, so you haven't awarded anything yet and you haven't punished the defense for their infraction either.
Yes, the runner chose to go home or was sent home by their coach; however, the bang-bang play at the plate was only possible because he was slowed down by F6.
In spite of an offline and low relay throw from F5 (because he had to rush it or he would not have had any chance at all), F2 slaps the tag down for a very close play at the plate and PU calls our runner out on a play that could have truly went either way even if there was no OBS by F6 ---- but, OBS did occur (we all agree it did, there is just some differing of opinion on how to award it) and now we need to penalize the defense for their infraction. If the play was that close at the plate and he's out by a hair due to an amazing relay, catch & tag by F2 at the plate - then do you honestly believe that if R2 was allowed a half-step or two more (it's more likely he would have covered much more distance than a few feet) that he would not have scored had he not been bumped by F6?
Something else to think about, how many guys at this level would not score on a hit to LF given a running start/lead off from 2B? There's a reason it's called scoring position once you reach 2nd base. If a ball leaves the infield in MLB, HS, Babe Ruth, LL, etc. - how many times does an average runner not score from 2B barring OBS? I can tell you they will score far more often than not barring a very good LF who made a very good read on the ball and a strong & accurate relay. In my personal experience, I'd guess 75-80% of average HS runners would score on this play without any OBS, so I'd have to believe that OBS on this particular play would have resulted in a run scored as well if F6 hadn't gotten in his way.
If you truly believe that he's only covered to 3B and he was only out because he pushed it and tried to score, then there's nothing more I can say.