The Avalanche is a 2002, Z71, tow package. Engine is 5.3L. I believe the gears are 3.73. I realized the trailer weight would be higher for the very reasons you said; awnings, a/c, propane,etc. And personally the more I can be under the max tow weight the better.
WV is pretty much all hill so there will be some grade climbs although at least for the this first summer I don't see us going into parts of the state with steeper, longer grades.
If all else fails, my son has a new pick-up with a 9,500 tow rating he has said I can use.....of course I think he is plotting to use the camper in return!