I'd like to try one of these on my 9.3 double as well, and/or perhaps on my barrel set in 7mm/12g. Anyone tried one?

From their website:

Trijicon RMR™

When precision is the only option, your best option is the Trijicon RMR™ Sight. Built to provide optimum red-dot visibility against the target, you can acquire and hit your target quickly and more accurately.

The new Trijicon RMR™ (Ruggedized Miniature Reflex) has been introduced to match the legendary toughness of the Trijicon ACOG® (Advanced Combat Optical Gunsight).

It can be teamed up with the ACOG® or AccuPoint® for the ultimate in fast target acquisition or precise aiming at extended distances.

The RMR™ offers two illumination configurations. One choice is an innovative LED (light emitting diode) insert that automatically adjusts for brightness in any lighting situation and ensures optimum visibility of dot against the target. The second option is a dual-illuminated, battery-free model featuring Trijicon fiber optics and tritium. Accuracy is further enhanced with adjustments for windage and elevation and clarity is assured with the sight’s ultra-clear, hard-coated lens.