Find a wooden dowel that fits in the post hole tight,flush it to the playfield.
Get a nice sharp forstner bit the size of the t nut
Put the pinpoint of the forstener in the center of the dowel you placed in post hole run the drill backwards slowly to cut the clear and into the art.
Once you are confident you are past the cosmetic surface and can proceed without damage run the drill forward to the depth you will need to countersink the that nut.
It is a risky procedure make no mistake but this is what I do when t nut recesses are missed but the holes already exist.