The two lowest I've tried on the Vinci are the Warne Maxima and Weaver multi-slot tactical bases. The Warne comes in both one and two piece styles and seem to sit the lowest. Drawback with the Warne is that it only comes with two slots. If you use the two piece Warne it would make a nice clean mount using only the rear mount. The Weaver sat almost as low and is a one piece multi-slot rail. There are other mounts out that will fit also, but those were the two I actually tried. This was with both a Bushnell trs 25 and also a Burris ff3. Not sure how the Rmr mounts but I imagine it has a weaver/picatinny base so it should fit fine. Sbe2 and m2 bases will fit along with Remington 7400-7600 bases. Hope that was of some help.
