Bike hitch on enclosed trailer with wooden floor

So I am moving to lower 48 from Alaska. My 17 foot enclosed v-nose trailer will be full of boxes, no room for my bikes. I'd like to add a hitch to the trailer to hold my Yakima 4 bike rack. I found a bumper hitch that attaches with bolts but the floor of my trailer is wood. Travel trailer has a ramp door in the back so not much there to attach to.

I am going to go by a machine shop today and talk to them about making a metal plate with holes that line up to the bumper hitch. Then I will put the plate on inside of trailer bolted to hitch underneath with a wood sandwich in the middle. Will this be sturdy enough to carry my bikes?

4 Bikes plus the rack weigh at the very most 250 pounds and that's assuming each bike and the rack weights 50 lbs which they don't. Bumper hitch tongue weight is rated 350lbs btw.

Any thoughts? I thought about attaching to front of truck but it's going to be hot (and a 3400 mile drive) and I am worried about not enough air flow and truck overheating.