As Campfire said, you need to check your payload.
However, the 5.3L is perfectly adequate towing that weight.
Can you fit all 6 of you in the truck? I am assuming since you have a 6.2L, there is a center console and no seat in the front. But just want to verify.
Palomino SolAire 307QBDSK
2016 Chevrolet 2500, CC, 6.0L, 4.10