Maybe this will help
Not sure if this will help, as I have no idea if our microwaves are installed in a similar fashion. I've attached a picture of our galley, which shows the enclosure that the microwave sits in. We're in the process of replacing it, as the old one recently died. No issue with the trim, as it was held in place with four clearly visible stainless steel screws, one at each corner. The microwave itself had a piece of plywood screwed to its bottom (it looked like a scrap of teak veneer ply probably left over from the interior cabinets). The factory had taken out the machine screws that held the four rubber feet on the bottom of the microwave and run them up through holes in the piece of plywood and then back though the rubber feet and into the original holes in the microwave. I suspect they probably used longer machine screws than had originally come with the microwave, as I don't think the original ones would have had enough length. They then sat the microwave in its enclosure and used a pair of pan head stainless sheet metal screws from underneath the fiberglass enclosure up through the fiberglass and into the plywood attached to the microwave. This holds it in place while the boat heels and moves.
Hope that helps, but if not, good luck.