Ed, I would be reluctant to break the ice, only because you don't want any sharp pieces to gouge or scratch the gelcoat. That would be my main concern.
Not sure about Ed, but fore me the temptation would be ..... simply because it's there. Like all the things I was not supposed to do when I was a kid and I did them anyways.
I suspect the main concern would be that if you lower the water level enough, there would be no support for the ice shelf, so if it broke-free awkwardly or at once and collapsed, it might scratch the gelcoat. Might only drop a few inches, and this whole thing might seem like a stretch, but that's the only concern I can think of. If lowering the water is the better choice as opposed to letting the pool overfill, it may be worth it. Maybe punch a few spots around the pool perimeter about a foot or so away from the edge to help relieve that pressure? I'm a bit outside my comfort zone, but that's what I might consider if I was in your place. Maybe someone else will have a physics scenario of their own.
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