What happens when a vehicle you want to trade-in is worth more than the new vehicle you want to order? would you walk away with a new truck and cash? or do dealers not want to trade like that?
It should not be difficult to sell your Ram privately. They are a very popular truck and there are many people looking to buy them. Then you can go and buy the other truck with no trade which gives you more bargaining power as well.
The biggest hurdle to selling something worth that much money privately is to avoid the scams and find a buyer who actually has the money or access to it. It can be done though and I think you will be much better off going this route.