Need more top of truck bed clearance

[multiwire]

I'm new to this Forum and recently purchased a Montana 3121.

My pull vehicle is a Chevy 3500HD, LTZ, diesel, 4WD, standard box, with 20" LT275/65/R20 Wrangle tires. I only have 4" of clearance from the top of the truck bed to the bottom of the 5th wheel.



My previous truck was a Chevy 2500HD, LTZ, gasser, 4WD with LT265/70R/18E tires and I had 6" of bed clearance!



I hope one of you guys can tell me how to get 6" of bed clearance and still have the Montana tow level.

Thanks