Worrywart.
It sounds like building my old Victoria. You built a plywood box, then screwed the servos into it, then glued the whole thing into the bilge. The box fit through the hatch with nothing to spare.
Huh - servo tape. Huh. I dunno! That stuff is pretty strong, but I've never seen a winch setup like that. (For what it's worth, my Hitec drum just destroyed its rather light plastic mount when a sheet hung up...danged genoa anyway!)
Oh...wait..... I take you're screw-mounting the servos into the tray, then taping the tray into the hull? If you've got enough contact area between the hull/stringers and the tray, I think that would work.
My EC12 - beasty servos. Gigantic custom arm winch, quarter-scale servo for the rudder and another quarter-scale servo for the jib trim - is mounted like this:
Radio board has all the servos screwed into it. Thwarts (side-to-side) pieces made from spruce are held to the hull with what looked like strapping tape (that clear tape with the strings in it?) or fiberglass cloth and CA. The board was then screwed to the thwarts. That lasted only about 20 years or so
I say tape or 'glas cloth only cuz it's unidentifiable - the boat's 20 years old and the material, whatever it was, just gave up.