In my case always unclamped (in fact I always use an undamped arrangement which is not recommended for clamping).
It really depends whether the listener is of damped or undamped persuasion. Not that I’m suggesting that a damped approach cannot work well also. I know one or two that do.
The mat in question is the “Gold Spot” hybrid Ringmat (hybrid because it features a 1mm latex underlay – which was always the basis for the well known Ringmat adjustable VTA/support system). The GS was mainly purchased for its greater manufacturing integrity than the more basic 330 Ringmat rather than for the “Gold Spot” itself ;^)
The platter is similar to yours, several inches thick vinyl-like impedance “plastic composite” platter (formula a trade secret…) ;^)