I also have a 12' trailer (dual axle, dual brakes, 5,000lb gross, 4,300lb net.) The BX "fits" but is tight; the FEL sits over the front lip and the BH has to be swung to one side to fully close the tailgate/ramp.
I would caution you on getting too "heavy" a trailer:
1. It will tempt you to overload your truck.
2. Too big a trailer will actually decrease the amount you can move. You need to keep in mind net load. Most steel 7k trailers weigh 1800-2200lbs which means you can tow an additional 4800-5200lbs. If you get a bigger trailer that additional tare weight eats into your capacity.
Good luck!