Not sure if the GCWR goes up if you go to a 4.1, but towing weight does increase. You did not give the dry weight of the 5 er you are thinking about.
If you go over 10k I would consider a diesel for a TV...I like the long bed for a longer wheel base...along with the crew cab....give a very stable tow with a gas truck in all conditions.....but trailer is under 10k loaded.....good luck
IMO don t just get by with a TV....bigger is always better it only takes one time not having a big enough truck to pull with to have serious problem.....