While here in Mi we don't have the mountains, we do have a few hills and a couple slow, steady grades. Having owned a '10 Chevy 1500 Silverado CCSB 5.3/6spd/3.42 4x4, and towed ~7200lbs, I never felt I NEEDED more power, just more payload. We were about 200lbs over the gvwr of the truck when all loaded up and ready to go. Under the axles ratings, by a little.... Main reason we stepped up to a 2500HD.
It all comes down to payload. The more you can load in the trailer, keeping as much near the axles as possible without making the tw to light, the better. Will keep weight out of the Burb. To light of a tw can, and will cause the trailer to sway. Which can lead to a very dangerous situation. That's what we used to do. When we could take it, I loaded firewood in Rubbermaid totes, and placed over the axles, with the front tire extending in front of the front axle a little. Making sure I didn't load them to far back, decreasing the tw. Then the coolers in front of the wood totes. My better half wanted the totes out of the trailer, which led to a new truck!!! Lol
Without going back a lot of posts, how old is your kid? And you may have another? I ask because if the original trailer, and a 2500/3500 gas motor truck is possible, I would bet you would not trade a bunkhouse trailer until the kid(s) are older and not camping with you very much. So that combo should last at least 8-10yrs with the proper care. Just a thought!!!! Not sure about my wife, but my tentative plan is to keep our current trailer for at least 8yrs, give or take. Our twin boys would be about 20 at that point, and hope the value of an 8yr old trailer will still bring a little money. And decide what floor plan will work for us at that time.
Keep looking, I am sure you will find the right trailer!