[Rog]

Especially since, the unsportsmanlike act(s) directly contibuted to the balk; which, allowed a R3 to score and advanced the possible tying run and maybe even the winning run. Be that as it may.....

Per Fed. Rule's: 1-15-1, 2-15/27-1-g, 3-3-1-g-4(*Penalty!), 4-4-1, and lastly 10-2-2/3-f-g-h, considering these, it does not appear that a "forfeit" can be made - at this moment at least!

But, in light of this "mandatory" pre-game statement which is to be given by the umpire(s):
"New York State Public High School Athletic Association requires Officials to enforce all Rules regarding unsportsmanlike conduct by coaches and players. There will be no tolerance for negative statements or actions between opposing players, especially trash-talking, taunting, or baiting of opponents. If such comments are heard, a penalty will be assessed immediately. We have been instructed not to issue warnings during the contest. It is strongly suggested that you remind your participants of this policy."

It would seem that the Fed. umpire is bound to rule according to the rules as written.....and, since under rule 3-3-1-g-4 Penalty provision the warning was issued during the pre-game; which, the player's violated = FORFEIT!!!
Score = Visitor 02 / Home 00

If, it wasn't a forfeit; and, since the manager/coach is hardly going to admit that this was deliberate, I would negate the Balk call, wipe out R3's run from scoring and put R3 back on 3rd, then dump R2 and R1 for their unportsmanlike conduct. It would seem that the offensive manager/coach is more than likely going to say something which would require their early dismissal as well.
Now, let's play - if we still can..... from here on in you can almost bet that every pitch "against the batter" you will hear a "moan", indicating that that you must be deliberately calling a larger zone, "to even things up"!!!

Now, OBR - is a different matter:
4.15
A game may be forfeited to the opposing team when a team_ (b) Employs tactics palpably designed to delay or shorten the game;

9.01
(c) Each umpire has authority to rule on any point not specifically covered in these rules.

and, that's my story; and, I'm sticking to it..... well, for now at least!