Here is an idea for a warm, lightweight floor. I got this idea when I wanted to make my basement usable. It had a rough, uneven concrete floor so I installed those square, interlocking garage floor foam pads that you can buy at WalMart. Laid them right over the concrete as is. This worked amazingly well! Dips, trowel marks, flaking, chalking, all disappeared. Instant finished floor! Cost: $250. And you can get various colors. Insulating quality is so good I can sit or lay down on the floor.
So I thought, "Why not do something similar in my new foamy TTT?" First make a wood frame (2x3" would be good) that is the size of the outer perimeter of the TTT floor. Then stretch galvanized metal mesh (also known as hardware cloth), 1/2" squares should be good, across the frame; stretch and fasten it tight. Lay a sheet of polythene over the mesh for waterproofing, tape it to the frame. In high traffic areas lay down 1/4" fir plywood or hardboard (or use a second layer of mesh) for extra rigidity. Then lay the interlocking foam squares right on top. Nice light, insulated, finished floor. For extra insulation, use two layers. (Each layer is 3/8" thick.