At this for two years and I bounce between 7/8th and JV assignments. 7/8th are more prone to this issue because of more held ball situations but very frequently the players continue to wrestle for possession of the ball after the whistle to stop play has sounded. This botheres me because that type of competition gets the emotions going and is a stimulus for other rough play. My solution:
Point of emphasis during Captain's pre-game meeting
Point of emphasis during Coaches' pre-game conference
Warning to all players during first held ball.

Unfortunately, none of the above worked and at the next wrestling match after the whistle I whistled both players for Double Technical-unsporting conduct.

1000 yard stares from both players and both coaches but it seemed to work for that game.

If players haven't been coached accordingly, the pre-game warning may have been/be a waste of time. Any thoughts on how this situation might be better prevented or controlled?

Make sure you (and your partner) close in when the whistle is blown-- with voice indicating "easy .. play's over" or something.

Expect that they can't stop immediately upon hearing the whistle -- sometimes one stops sooner than the other and is pulled over by the other. Judge whether that's a result of some "action" that started before the whistle.

There's a fine line between blowing the whistle too soon ("c'mon -- let'em play") and too late ("someone's gonna get killed"). You might be a little on the "too late" side -- that's when the "extra" wrestling comes out.

Bob's right on target; but I'll just add that if you do what Bob suggests and the wrestling continues b/c you've got hotheads/pinheads, I have no problem with the double T's.

I read a post around here a while ago that suggested you close and keep blowing your whistle, the idea being that a Fox40 in the earhole should cause both players to lose interest in the held ball and cover their ears. Haven't tried it myself, but it might help your situation.

Another technique that I have used in similar situations when players seem to be getting out of hand or too physical is to wait for the next dead ball and call both coaches to the table. I then tell them that the rough play has to stop and that I only have one way to stop it: my whistle. I then add that the coaches can talk to their players and end the situation. I make it clear that if the play isn't cleaned up, they will be hearing many more whistles and having players DQd. It almost always works.