Yes a toyhauler will work, and that would offer a couple of large sleeping areas too. Actually the minivan idea is ideal, in that you are putting about 750 pounds into the minivan in people and bikes, that will not need to be carried by the E-350. You only have so much cargo rating - even on a E-350. Have you checked it's weight on a scale? You might be way over the 9,600 GVWR of the van, and the rear axle especially might be overloaded right now.
My other suggestion is a couple of 4 bike carriers. You can get a front hitch for the E-350 and carry 4 there. You can get a A-Frame hitch for the trailer, and carry 4 more there, but I would put the smallest and lightest one's there because it is swinging a lot of weight high above the hitch, and in the air, and putting additional weight on the Van's already loaded hitch.
You can get a bumper mount hitch for the trailer, and carry 4 more back there, or put on two mounts, and somehow carry more bikes!
ETrailer.com sells a A-frame mount for a 2" receiver that can hold the 4 bikes way above the propane tanks.
They also sell the front receiver. And 4 bike carriers.
And perhaps a trailer mounted receiver that can carry another bike rack.
They also sell roof mounted racks, if you want to start taking along a 6' stepladder?
Or start putting them in the trailer? I put my bike into my camper before buying my motorhome.
On my motorhome, I tow a car, and removed the factory hitch, had my buddy weld on two each 2" receivers. One for the bikes and another for my SACCO dog cart.
Good luck,
Fred.