Without some sort of barrier, the sand on top of the clay will quickly mix, and it will be all clay again.
I don't like the tarp idea myself, as once it gets caught and pulled in something (boat anchor, mower, etc) it will be a pain in the butt to deal with it. Think kids sand box on how they always get a pulled liner and then you have to pull the whole works out.
I like the old carpet idea with sand on top. The carpet acts as a barrier, and the texture should keep sand more or less in place. Adding SoilFloc on top of that... glue. With the carpet out of the direct sun, it should last longer than you, and when it snags, it will just rip, not pull up from the bottom.
