i have an '07 Avy 2x4 with the 4spd tranny and tow package.
i have a 7200lbs. towing capacity and i tow a HTT that is about 3' shorter and 700lbs. lighter.
i have no problems and feel it's a well-matched combo.
i have the 1000/10,000lbs. Equal-i-zer and love it.
since you have the newer 6spd. tranny, you should be fine, especially since you don't have the mountains we have out here.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC