Beyond the pond,
Sorry to hear about your leaking pond!
The fact that it drains almost completely does suggest a "bottom leak" rather than a levee leak.
However, it is possible to have a bottom leak without ever excavating to sand. You may have gotten very unlucky and you have a sand layer or stringer just a few inches below the clay at some spot in the bottom of your pond.
The bottom of the pond should have been excavated 1-2' DEEPER than the design depth to discover all of the sand deposits, old tree roots, and large rocks. It is then back-filled with good clay, moistened, and compacted in 6" lifts. The bottom clay blanket should be at least 1' thick on a pond with a water depth of less than 10'. (Even thicker is better if you have enough clay material.)
If the pond is deeper than 10' at full pool, then it probably should have a bottom clay blanket of at least 2' thickness.
How deep is your pond by design? Do you have "extra" clay in the levees that comes from the spoils that were excavated from the pond site? If so, then one option is to dig up the bottom of the pond to find your leak (probably in sand), and then re-seal with good clay and proper compaction equipment.
Unfortunately, that option is going to be expensive. As mentioned above by Bob, TJ does have a remedial process that frequently works for leaks like yours. Hopefully, TJ will drop into your thread when he gets caught up on his fall projects. (If you don't see him reply in a few days, then you might want to send him a private message to look at your post.)
Good luck on turning your "leaky hole" into a pond!