So you need to haul the bike and the trailer at the same time, correct?
My concern would be damaging the tailgate when turning too sharply. If the trailer sits low enough to stay under the tailgate, it will be no problem. If you have clearance issues, I would remove the tailgate all together to avoid the possibility. You may have to angle the bike corner to corner in the bed of the truck so the rear tire has something to sit on. The front of the bike will compress as normal, then use 2 more straps to keep the rear of the bike all the way to the side of the bed. The rear straps don't need to be very tight, since they hold almost no load.
Lousy picture, but you get the idea:
The other thing I have seen people do is leave the motorcycle ramp under both tires of the bike, thereby extending off the rear of the truck, and under the rear tire of the bike. You will need more tie downs to keep the whole thing from sliding, though.