I previously towed our 28'er with a Chevy Avalanche - essentially a 1/2 ton Chev Suburban with a pickup bed instead of a third row seat. While that vehicle was perfectly adequate for towing on our flat Florida terrain, I wouldn't have been comfortable with it in the mountains. I traded up to an 08 Chev 2500 Duramax and it is night and day difference, for the better. Probably more truck than you actually need for your trailer, but your braking issues seem to me to be an alarming problem. Stopping when you need to is a lot more important than going when you want to. Even with a brake controller, the mass of your tow vehicle greatly affects stopping power. In addition, with the Duramax you'd gain much larger brakes than on your Armada or even than what you'd get on a larger suv like a Suburban. I LOVE my truck and am so happy I traded up. The ride, unloaded, is a little rough in that I use my truck as a daily driver, too. Given your mountain driving, and that you won't be using it as a daily driver, I think the 07 Duramax sounds like the perfect thing for you.
'06 28' Safari SE / '08 Chev 2500HD Duramax
'64 Me / '60's-ish wife / '90's kids / '06 Black Lab / '02 Poodle / oh, and a horse, too.