I had the same issue. Clay soil and I hit water at 2’ down. What I did was put a pipe with slits in it, much like what you would put in the bog, at the lowest part of the hole. I actually dug down another 6” and put in a 2” bed of small blue stones, then set the drain pipe in and covered it with more stones until it was level with the bottom. I then ran the pipe up and out the side of the hole. Because I hit water, I ended up building a wall around the hole at ground level so my pond is half in and half out of the ground. I backfilled around the wall with the dirt from the pond. This works great because the drain outlet is lower then the pond surface level.
This is the important part. For the water under the liner to escape without a pump, the outlet must be below the pond water level. With this design, the water pressure in the liner, forces the water under the liner up and out the drain. Hence your reference to hydrostatic pressure, if the water under the liner has no way to escape, it will balloon up the liner and force the pond water to spill over the edge.
Since I had clay on the bottom of my pond hole and it was very soft and sticky after I pumped out the water, I used concrete to cover the bottom of the pond at the lowest level and the sides where the water had eroded the clay. Only about an inch of cement since it was just so I could get the underlayment in without getting stuck and making footprints, I also cut a Lowe’s blue tarp to fit the bottom of the hole so I could walk in there without the clay mess. It worked great, got the underlayment in and the the liner without a clay mess. And now with the pond filled and doing great, when the rains come and the ground water rises, the drain let’s the water under the liner run out.
Hope this helps.