I have to chuckle a bit at your optimism... "leaking isn't even possible"
Lots of folks here with lots of good clay but still due to improper compaction, improper construction of the dam, the base keyway, etc have a leaks.
You could consider a sand layer on top of the clay and then adding a polymer that grabs the granules of sand and binds them together into a hard surface (research soilfloc on the forum)
Of you could do as you suggested and add some type of setting cement.
