My guess on this is you would need to dig a trench deep enough to go way deeper than the old dam which is then the new key. This needs to go the whole length. Then pack the new key and trench all the way back up to top surface with good clay using a sheepsfoot roller.

I also wonder if it would be a possibility to put a keyway and new dam on the backside of the current dam, providing there is enough room and you would have enough available clay.

There was an old thread that I read where one pond builder (was it Otto?) said that sometimes you can dig out and then repack with clay a wetspot from the backside and it will work. That thread talked about doing just this and how it worked. My thought is that it's iffy.