I don't post often but geez. Diesel this and diesel that, blah blah...
A diesel in many instances doesn't instantly add up to much much more payload/capability. And for many people such as myself, a diesel just isn't a viable option. For instance, my truck is also my daily driver and I live about 8 miles from work and tow about 6-7 times a year, once maybe twice I tow 200 miles but most of the time I'm only towing around 30 miles on flat road. I have a 2015 Silverado 2500HD gasser with just slightly less payload than the OP.
11,000 lbs.? Are you kidding? I'd be just fine towing that! Up the steeper grades my rpm's will run up but who cares? That's what it's designed to do. How often are we all climbing mountains around here anyway?
Many more things come into play to decide if a diesel is worth it to people. As long as your within your capabilities, have at it for Pete's sake.