IMHO, the best performance sandbox won't have a top cover. If you won't accept having your TT laying in the sand, then 4 circular legs (brass or steel prefferably) can form a "civilized" base on top of the sand.
Why leave the top free? Because the free face of the sand in the air allows it to vibrate freely and release more energy in the air, rather on the TT.
Why brass feet rather than glass or plywood? Because it's an interface of materials and you WANT each such interface to act as a mass absorbtion system. Plywood and settled sand have rather similar densities. Brass and steel are much denser.
I would invite anyone currently using a sandbox to just remove the top cover for listening to the TT.
PS. Last night (it's early noon here now), I recalled another mod for the improvement of the sandbox. Assuming the sandbox can contain 3-4" of sand, you can have the first layer (first 3") contain a mixture of sand and rubber pellets. Pellets have to be small (3mm, i.e. 1/8") and soft. The top layer (at least 1") must be pure sand. The bottom layer must be leveled and settled before the top layer is added. And, the thicker the mdf or plywood forming the sides, the better - less vibration comming from the sides.
The small rubber pellets allow the vibrations comming in the sand mass to be absorbed faster and locally, rather than travel towards the top and being gradually attenuated.
20 years ago, such material studies and sandbox designs were very fashionable. I even found an article in an IEEE issue, while I was searching for loudspeaker design methods. Not much of that has survived into the internet, I'm afraid.