Sell to dealer: Immediate and done with, but will sell at a lower price.
Sell privately: Can be time consuming, but can get a higher selling price.
Sell privately has one other risk: the longer your camper sits for sale, the less in value it becomes. When selling privately, you really are gambling on time.
If you are not in a hurry to purchase that new camper, then start listing it privately now. If it sells quickly, you have all to gain. If it doesn't sell quick, and you are not in a hurry, then you have the luxury of time, but also a depreciation in value the longer you wait.
And then, if you reach the end of your expected time (say 1 year wait) and you still have no private sale, the camper is now even a year older. Take it to the dealership for a trade now, and you'll get even less.
Personally, if the goal is to get a different camper, do the dealer trade, eat the loss and move on. You're done with the frustration and you can get on and enjoy camping.
Too bad about that Outback. You're giving up a darn good trailer!