I hope Otto will chime in, way more experience, I know just enough about dam building to be dangerous, I think your biggest obstacle is do you have enough clean, rock free clay, available to you to actually get your 2ft + layer of clean, sealing, well packing clay to line or cover the rock with, if so I think it can be done.
If it were me, any rock exposed in the core trench I would clean off as best as I could and add copious amounts of bentonite.
I actually sealed off a little pond that was leaking in a similar situation, when digging down thru the dam the only water I found seeping was right down at the shelf rock layer. I cleaned the rock as best as I could and put a bunch of bentonite, plus a little more mixed into the dirt in the first several layers and packed it back full to the surface with the cleanest clay I had available and it seemed to work great, thats been 12 yrs ago and as far as I know its holding fine, the property was sold several years ago so I haven't had any feedback for a couple years but the original owner was a friend of mine and was tickled with he out come.
