Dan, my TV setup is nearly identical to yours and my wife and I have had as many as three older teens with us.
Bikes for me have always gone into the bed. I take off the front wheels and use bicycle
skewers to stabilize the bike. You can also use a truck rack and hang them upside Down if you wish. I use a
TracRac and have had kayaks on top and suspended bikes below. (Thule evidently now owns TracRac, they cost nearly 2x what I paid for them.)
Getting a receiver welded onto the front of your truck may be a good idea too, I've seen bikes carried that way.
I'd keep them off the trailer though for the good reasons already posted. Chucks point about metal fatigue is valid.
We go to Hatteras Island every year and stay at Camp Hatteras. June is a great time to go. Where do you plan to stay?