I made the move from a 25 ft. TT to a 31 ft. fifth wheel for camping scenarios similar to yours. We are overall happy but realize there are tradeoffs. The fiver tows shorter and is more comfortable on the road. Storage on the fiver is ample and more easily accessible than the back of a truck. Backing takes a while to learn, something I have not completely mastered.
A word of caution. Your truck has tailgate height of 60" or more. Early 2,000s trailers were built to fit the trucks of the day which were lower. Take a tape measure and measure the overhang of your prospective trailer and make sure it will fit your truck with sufficient bed rail clearance. Many won't. There is no way my 2008 trailer will fit your new truck. Click my profile and cross that model off your list.
Good luck and have fun with your search.