My husband solved the warping problem with a sheet of 3/4" masonite board. It's heavy, but it works. He built me a table that it covers. It's 3x4 ft - I used an old wool blanket on mine, just under the padding which is the padding made for hot pads. Then I used regular old everyday muslin and put a gridded cover on that. I use a staple gun when I have to recover. The grid fabric I get from the fabric store. Works great.
Then I made a board to carry with me when I go away - even has a carrying handle. It's about 2 ft by 15/16 inches wide, and even has little feetsies so it won't slide. Perfect. Then, I made a third one, about 12x12 inches to sit beside my sewing machine. Love to iron !!