I have the same setup, except me truck is a 2011.
Me hitch is all the way down and the kingpin (trail air, the one with the air bags) is all the way up.
I have a long box with a flip cover.
I have about 6 to 7 inches clearance between top rail of the truck and the
overhang of the trailer.
The trailer is slightly nose high, 38 feet trailer length, measured front and back to road surface, about 2 inches higher in the front.
I hope this helps.
If you really nose high, the only correction you can do is install bigger rims/ tires on the trailer.
I'm thinking to replace my present trailer tires with LT Michelins next year, they are about 1" bigger in their I diameter, that should help me to compensate the level of the trailer.