TBH, I don't see a point in selling the Raptor and buying a new truck if the payment will be equal or higher. Not to mention when you go house shopping your total loan would be higher and have more term left than the Raptor.
The newer F-150 will have a greater depreciation drop than the Raptor, and it's not a Raptor, so you'll have a higher payment on a truck that may not be up to your standards/wants.
Either go used, but one still in warranty/CPO range, where the initial big depreciation hit has occurred or go with an econo car short term. Then once you buy the house you like, then you can go back to a fun vehicle in a short time.
Also, look up values, auctions are the best if you can find those numbers, and go to multiple dealers if you want to trade it in/not deal with private sellers. Could get a mini bid war going on.