OK, I'll play.
Don't just think of the space in the back of the trailer, think of the weight and where it will be positioned. There was a long thread or two about a conversion of an older trailer to make a toy hauler. IIRC it was wrecked soon after completion.
When Airstream built the Pan America they considered axle location to compensate for the additional weight.
The Pan America was a 34 foot trailer. It had a rear garage, 11 foot long, and fairly wide but limited by the hatch access. A Morgan Plus 4 is just over 12 foot long I believe, and wider than the hatch. The trailer could conceivably be modified, but sounds like a lot of work. And this is a 34' trailer, not a smaller and narrower trailer as you mentioned.
Great thread here on the Pan America, to get you thinking
You can carry the car on a flat deck behind the truck cab, but not on an Avalanche.
A Morgan three wheeler would be easier to fit in.
When I had a Plus 4 some years back ('97 model, Rover T16, Jaguar Platinum Silver over navy blue Connolly leather, with chrome knock offs, optional alloy wings, etc) I drove it to all the Morgan meets I attended. Side screens were a hassle, it wasn't a wet weather vehicle. After each trip there was a fair bit of cleaning. If I was taking it along on a camping trip I would want it covered. That is partly because I came back to it parked once, and found two kids under the age of five jumping on the front seats while Dad watched them playing. Photo attached.