Check the hitch ratings.
Most say something like 5,000 pound 'deadweight' and 500 pound max without WD bars. And 10,000 - 1,000 hitch weight with the WD bars.
So you will have much more weight rating with the bars on. And I also think that your 650 pound estimate is way off. Only taking it to a scale will give the real numbers. Once you get the total front and rear axle weights with the WD bars loose, then drop the trailer in the parking lot, and check the truck weight alone. This will give you a new exact weight of what is on the truck. You might have as much as 1,000 pounds on the hitch, if there is a forward fresh water tank that is full.
As for fifth wheel selections and a 2500 series truck, you might be limited to the smaller and lighter fifth wheels. The only large fifth wheels that I know of that are towable and still under 2,000 pounds hitch weight would be the Glendale RV Titanium series trailers, and they are not in production anymore.
Yes you will enjoy towing a fifth wheel more than the travel trailer, especially in high wind conditions.
AS for sway control, I would keep using it. The way the 'electronic' sway control works is applying the trailer brakes to bring it back inline with the truck. So who wants the trailer brakes applied constantly to keep the trailer stable? This will reduce gas mileage. . . .
Have fun camping!
Fred.