Interesting End to Game
 

High School game between rivals. Game tied 1-1, bottom of 7, Bases Loaded. Base hit to RF should end the game, but R3 does not touch home before running towards first base along with teammates from 3B dugout to congratulate BR. HP Umpire does not signal safe and remains standing behind the plate. After considerable delay, DC sees HP Umpire, realizes what must have happened and begins yelling "Get the ball". This warns both teams that the run has not yet scored. R3 beats def player with ball to HP in very close play. HP Umpire signals safe to end the game. DC asks why R3 is not out for "leaving the baseline". HP explains that only applies if runner is attempting to not be tagged. DC asks if runner is out because teammates have come on the field. HP answers "No". At this point both umpires leave the field. DC approaches HP in parking lot (in very courteous manner) and asks how to file post game protest. I suggest he ask his Athletic Director.

Any suggestions on how it might have been handed differently?

What if nobody notices that run has not scored? When do you call runner out for abandonment (upon entering the dugout)?

What if: instead of yelling for the ball, DC had "Appealed" to HP that runner was out for missing the base ?

Once the runner left the area of the plate the umpire should have left the field, unless stopped. Do not just stand there waiting for someone to do something. Treat it just as you would have if the runner had touched the plate.

The runner is assumed to have touched the plate, so he can never be out for abandonment.

Once the runner starts returning, the defense can't make a dead-ball appeal (in this situation).

Again, this is coming from a softball umpire who does very little, baseball, but only at the youth level, using NFHS rules.

Once the runner missed the play and no play was being made on the runner who missed home plate, the PU should pause momentarily, then signal safe. It is up to the defensive team to notice and properly appeal the missed plate. The slight hesitation could be a clue to the defense the plate was missed. If the defense does not know the runner missed the plate, the PU, by waiting and standing there is in fact aiding the defense by letting them know that the runner must have missed the plate.

No need to make a signal of any kind. Head for the exit, and if no appeal is made before you leave the field, it's too late.

Did R3 ever reach the vicinity of home plate of did he peel off 20 feet early?
Did BR ever touch 1b?
Did any or all defensive players leave the playing field?

Video
 

is this actual footage of the play in question?
If so am I to assume the first person coming across from the left of the screen is R3? If it is, he did not MISS HP. IMO, you must pass over/by a base in order to be assumed to have touched it.

I'd classify that as a gross miss but it still needs to be appealed.

That was not handled properly. Umpires should have been heading towards the exit once both teams came out on the field like that.