Seems to me that if you don't want to sell yourself, take the Camping World offer and go to whatever dealer you want to with a $15,500 down payment. The dealer doesn't care what the NADA value is. They are only concerned with what they can actually sell it for. It all ends up being a shell game. They agree to give you another $1,500 for your trade and then don't come off the price as much. It doesn't matter which you negotiate first. If you negotiate the trade-in price and they give you more for it, they don't come off of the price as much to account for the extra value of the trade. If you negotiate the price first and they come off of the price more, then they don't give you as much for your trade. Remember that it is a business transaction. The dealer has decided how much they need from the deal and will not likely dip below that without some other outside incentive coming into the mix.
The other option is decide what you are willing to pay for the new unit including your trade and negotiate from the bottom line. For me, the only number that really matters is what I have to pay for the new unit. Then the dealer can put whatever number they want on whatever line as long as the out-the-door price is what you are happy with.
You didn't indicate if you have a loan balance on the current TT, but that could certainly weigh into the mix if you are trying to cover the balance as a part of the deal. I still think it makes bottom line negotiation easier because they still have to figure in the payoff with the deal.