Nsgarch,
I don't use a mat and I doubt many Teres owners do, especially those with hardwood platters. Cocobolo, jatoba and lead as implemented by CB are superb at resonance control. A mat would probably be counterproductive.
Dish-warped LPs are definitely a challenge to clamp when playing concave side up. The edges like to rise when pressure is applied. I've had some success by holding the edges down with two hands while tightening the clamp with my third hand. :-) Sometimes, with just the right amount of pressure, I can convince the LP to couple tightly to the platter even when the warp doesn't "want" it to.
When I had a periphery ring it helped a lot, but even then some badly warped records would not sit perfectly flat. I imagine only vacuum could achieve that.
The reflex clamp normally works very well. Many records literally must be pulled loose from the platter after the clamp is removed. Careful clamping has created a vacuum-like seal.
Cheers,
Doug