Either way, I think I would still have to core the dam.
I sure hope someone corrects me if I'm wrong, but if the entire pond basin is covered with clay or liner, then there is no need for redoing the core. If the water goes into the "bowl" it can't get to the core, so no need to fix the core at that point. The best fix, but the most expensive.
If we dig down below where the dam meets natural grade, I can't see how we could miss the dam leak.
Water works in mysterious ways... (actually not) - but it can do some pretty amazing stuff. Like being forced downward 20' by the weight of the water and then follow a vein 200' away to come out no where near the pond. If you know where its leaking on the backside I would tend to follow that vein back into the ground/dam and just try to put this trench you are thinking about in that spot. Perhaps a few feet in each direction out from it and downward. That would be the cheapest "gamble". This is just me being cheap... that's not always best.
