With a good synthetic you can even do 8k intervals with that load. I know because our GM work trucks with the same engine go 8k with a [censored] of alot more weight and UOA had always come looking good at that interval, the guys at BS even said to go for 10k OCI.
For that engine, 3,000 lbs is not huge. I was towing 7,000 lbs on my 08 3/4 ton 6.0 engine, requiring 3,5000 rpm up grades. Under summer conditions ( and possibly higher oil temps) I switched to 5w40. Going back to 5w30 this fall. After 10 years of using synthetic 5w30, I'm closing in on 200,000 miles. Runs great.