If you're looking at 13,000 GVW of the 5th wheel, (11,000 axle weight + 2,000 pin weight), I don't think a 20,000 GCVWR is going to keep you legal if your goal is to remain within all manufacturer's ratings! We tow a 13,500 lb GVW 5ver and are running 21,380 GCVW (21,500 GCVWR) and 10,480 GVW on the truck (10,500 GVWR) with fuel, passengers, cargo, hitch, etc.
Rusty