I've learned the hard way to "leave good enough alone".
With the fragile state of the paint and the lifts/flaking all over, getting any liquid under that is only going to weaken it further, to the point of even more flaking IMO. You would more than likely start a reaction you won't be able to stop.
My suggestion, if it's flat enough, have a round piece of thick plexi cut a slightly larger diameter and sandwich it between that and a piece of plywood for a backer, screw them together and consider it stabilized between the pressure of the 2 outer pieces.
Darin
