I did not think NY had State parks with beaches that had sand deep enough to bury someone in, in the manner you so describe and intend to do! I live in NY,Rockland County, not too far upstate, I know 7 Lakes and never found the sand there to have the depth to accomplish this feat.
Curious to know which state park you speak of but don't expect you do announce it here opening up the chance of being interupted or disturbed by unwanted intruders or guests HOWever, IF you care to induldge me, you can email me the location. Shygirl and I may wish to visit this place sometime if it is not too far from us otherwise we will just have to travel to the Jersey shore.
At any rate, good luck with your venture and look forward to your posts about it.
TTD