There are things that can be done to improve the ride of your current set up. A better description of jerky will help. Ie side to side sway, trailer is like tail wagging the dog, you feel pushed and pulled by passing vehicles, or I'm guessing more of a porpoising movement. You should be able to have a pretty smooth ride when towing if you are within specs of the TV. Generally you want to have 13-15% tongue weight so some load redistribution may help you. Also you may need to dial your hitch in better. These are all guessing games without more info. What is needed are tv gvwr, gcwr, payload from tire loading sticker inside your door (even better are actual scaled weights of your rig). What are your tt weights (scaled is best)? What model open range do you have?
I can't speak to how the fifth wheel tows yet as we don't pick ours up for another 2 weeks. As others have said finding a 5ers for an f150 will be tough if not impossible depending on which f150 you have. The ecoboost with max tow package can pull a 5er but most others really fall short of being able to do the job.