I don't see any issues with this combo if it's properly set-up. We are a few feet shy of 37' but our 3/4 ton tow vehicle does a solid job of toting our 10K# TT around the four corner states. No doubt tongue weight will and needs to be more than 1K# for optimum towing results. Just pick one of the better WD/SC hitches and once dialed in you should have a satisfactory towing experience.
For the exact same reason, our next rig we are going with a longer, higher-end TT as well. Those are some very nice TTs above, I like both Jaycos but the Grand Design's unit just appeals to me more. Today's TT floorplans are nearly identical with their 5er counterparts, and the plus is that a 3/4 ton TV can more readily handle their payloads. Enjoy your awesome new TT!!!