I would go with that plan and add some ratchet straps to the rear of the trailer to the bike rack somehow to help stabilize the bounce of the bikes.
Also look at the floor of that trailer from underneath and see where the floor joists are. Maybe you could tie into one or more of them while attaching the hitch.
By the way, we carried three bikes on the front of our 98 chevy half ton towing a 31 foot airstream loaded HEAVY for years and never had an overheating issue. (I would not hesitate to do it again but our new trailer has a built in bike rack from the manufacture.)
