What size tire do you have?
Consider the following:
You don't need LT E tires for your truck. You'll be bounced around and its overkill for your TV/TT combo. Also, I bet your rims could not support the 80psi.
If you go LT, than load range C is more than fine.
I'm guessing as to the size of the tire for your TV, but I see that the General Grabber HTS in a 245/65R17 in the XL has a max load of 2403lbs, which is decent. And, XL tires don't need to have a very high PSI, which is better for many of the rims today.
DW, 3 Kids and our Goldens
2012 Shamrock 233S
2008 Toyota Sequoia 5.7L 4WD