Couple of ideas (some of which may not be suitable for your specific item, but I can't see it right now to know how it attaches):
1) Epoxy some sort of mounting block to the cabin surface and then mount your item to that. This could be a pre-formed fiberglass block, or a wood block, for example. Note that Starboard type material will not epoxy well.
2) Use Weld Mount* studs (or stand-offs) and then mount your item with those.
3) Use 3M VHB tape.
Sunbeam
*Weld Mount is a company that makes metal studs and standoffs, and also things like footman loops, wire-tie and cable holders, etc. The bases attach with very strong methacrylate glue (which they also make). The main limitation on them (for heavier items) is what you are attaching to. Because, for example, if you are attaching something heavy to gelcoat, and the gelcoat doesn't have a really good bond with the substrate, they can just pull off the gelcoat. Of course one can potentially remove a "loose" surface in a small area underneath them, but the main idea is to just consider the weight and force (tension, shear, peel) you are putting on them (i.e. trim tabs would probably not be a great choice to use them on). Quite a few boatbuilders are using Weld Mounts now to mount things such as fuel filters, wire runs, etc. in new construction.