I think the biggest factor driving whether the trees stand or go is:

Can the pond builder seal the bottom of the pond to ensure it doesn't leak with the trees in place? If so, then I'd cut them off a couple inches above full pool mark and leave them. (so their location was visible)

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3/4 to 1 1/4 ac pond LMB, SMB, PS, BG, RES, CC, YP, Bardello BG, (RBT & Blue Tilapia - seasonal).