I feel for your pond emotions, and I sure hate to be a nay-sayer, but I'm afraid that thin plastic liner will neither last, nor work for very long, if at all. I had some experience several years ago with some similar failed ponds made with pool liner over sand, and covered with sand. It doesn't take much more than a deer wandering in the pond to puncture such a liner. I don't know the thickness of that liner, but pool liner is usually 20-25 mil.
I think that compacted clay is by far the best solution. I don't believe you will be able to put 6-mil plastic sheeting on top of clay, and then adding clay on top of the sheeting. It is just too thin and weak. It will probably puncture and/or rupture with the first load of clay dumped on top. Adding equipment to the equation makes it even worse.
I'm afraid that if you need a liner, it needs to be something like 45-mil EPDM aquatic liner. It is tough, and it stretches under stress. But, compacted clay is still going to give you the best chance of success.
