Update:
I'm coordinating the pond revamp with my parents (who own the property) and brother, and it seems I misunderstood the situation a bit. The current seepage isn't that bad, as there's apparently only a bit of wetness in years when we've had a lot of rain (which is kinda how rain works).
Their concern is that draining the pond (to de-muck and nuke the current LMB and BG population) would cause the dam to crack or blow out. I'll consult with TJ in the event that real leaks do appear, but in the meantime, the big question is:
In your experience, does draining a pond cause new leaks to form or cause dams to blow out? How do you view the riskiness of draining a dammed pond?
Right now, we have a very boring and unbalanced LMB and BG pond, so our dream of having SMB and YP, or anything different, is very dependent on being able to drain and reset, but for now my parents are terrified that draining is going to blow out the dam.