I use my glass topped dining room table. Do the center first, then I move it up or down and pin. I just keep doing it this way until it is all pinned. I use large safety pins. I have done this for many years and many, many quilts.
You could start at one side and work left to right. I always smooth as I go. When changing to another long area. I make sure backing is smooth, then batting and top.
The frame would work.