On a plastic boat, a 100W SSB generates significant field strength, possibly levels which we would not permit folks to be exposed to. Personally, I would not use an SSB on the boat very often. Emergency only.
Envious of your ride. Nice boat.
Speaking as an engineer, and an electrical one at that (I stand ready to be corrected by a mech eng), seems you have a resonance, and it's due to physical characteristics like lengths and masses. As to what is resonating and how it's being excited, I don't...
I'm a trawler novice myself, and would also appreciate some input. I'd suggest viewing the Camano Troll as well though. New Trolls are going to be produced now.