First...a big howdy from iRV2.
Personally, I'd bump up to the 6.0L and a 4.10 axle. The traielr will never be at the dry weight. Dry weight is a base number with no options or accessories. Any item listed as an option has to be added tothe dry weight. This includes, A/C unit, Micrwave, batteries, awning and any other option plus propane, some water and all of your camping supplies. It is not at all unusual for the loaded weight to exceed the dry weight by more than 1000#.
For the tow rating on the truck, this again is a number based on the base truck, no options, hitch, cargo or even passengers beyond a 150# driver. So for estimating purposes, use 80% of the vehicels tow rating for a loaded trailer weight. Your 7000# tow rating will evaporate to become 5600# for a loaded and wet trailer. This is way too close to the dry weight for comfort as the trailer will most likely be 6200# or up to 7000#.
have fun shopping and remember the number one rule fro RV or truck shopping...NEVER believe the RV or truck salesperson or dealer. His job is to sell trucks or RV's...not offer you advice.
You will find a few (and there are very few) delaers that understand towing and ratings.