After giving it some more thought over dinner, let me add a few things.
You might look at the Livin' Lite Camplite 13RDB. I don't know the interior height, but width of 7' will let you lie down. I believe it sleeps 6. Dry weight 2250 lb, dry hitch 180. By the time you load up, you'll probably be about 2800-2900 lb (GVWR is 3000) and you should easily be able to load it for 300-350 on the hitch. The Ody appears to have a CCC of about 1350 lb, if the numbers I found for it are correct. Subtract 350 for the hitch, that leaves about 1000 lb for the passengers and stuff. 6 adults could be problematic, but maybe some of your passengers are youngsters?
I've towed trailers of that size with my '08 Highlander for over 140,000 miles. 270 HP, a bit more than the Ody, but a noticeably shorter wheelbase than the minivan. I did have the advantage of 500 lb hitch rating, which allows more flexibility in that regard. Otherwise the two vehicles are similar in size and performance.
Some people I know of in Canada are having custom receivers fabricated for their minivans and with WD they are towing Airstreams with them. But I doubt they are carrying 6 people, unless some are little kids. Cargo capacity is still an issue. But Ody's are tough vehicles with great handling characteristics, good wheelbase, and enough power for most situations; like I said though, you'd want more power in the mountains.
