For OP with 30’ TT GM HD payload pkg or whatever they call it. Add 6.2 & 10 speed and you will be a happy camper so to speak. But your challenge will be the same as it was with Ram and that is selecting an appropriate WDH & built in sway control then learning to set it up by CAT scale results. Had that been done well you would of had no issues with the Ram either.
A 30’ can be safely towed with stability by the right version of any of the 5 1/2 ton Mfgs when setup is adjusted until you have A at minimum replaced your unloaded steer weight, B not exceeded your drive axle weight and C gotten your tongue weight in the 10 to 15 percent range.
The 5.3 would get the job done with the 10 speed but it will struggle in comparison to the 6.2 and use as much fuel to do it. The 6.2 will be much more enjoyable to tow with and more fun to drive when not towing. New truck fuelie results shows difference in real world economy to be small between them. Much like towing with the 3.5 EB being easier & more enjoyable than with the 5.0.