With the FN (flat pan), I've had great luck with binder clips. When I had the Martin's, and now, with my other SuperPet cage (cages with deep pans that you put the cage into), I put fabric down and then put the cage in. My smaller SP's, though, I'm at a loss with, as the cage fits right into the top of the pan!
My boys still try, but I have better luck then when I just put it down and crossed my fingers.
I have a huge Hutch type with 5 inch plastic sides, and the cage sits on top of the walls.
The only idea I had was; a perfect fitting board, with Melamine plastic coating on 1 side. I could lay the towel flat on the ground, lay the board plastic side down over then pull edges of towel over board pin down with thumbtacks.
This would work as the weight would also help keep the towel pinned, but the only problem is I would have to unhook and lift off the cage each time and its 40x20 30 and really awkward and heavy and I'd hate to go through all this every couple days.
I would try the velcro. When I had my boys in an aquarium (read enormus glass house with lots of levels) I used vlecro sticky tabs for their water bottle instead of the metal things and they would climb on it and everything but it never came down.