I have towed a 3500# GVWR, 7ft wide HTT trailer through the mountains in Wyoming and Montana with our 2003 I6 Trailblazer that has less HP than yours (271). Out Trailblazer has 150k miles on it with the original transmission and no axillary cooler.
We now have a 4750# GVWR HTT (Jayco X20E in sig) that rides higher and is wider than the old HTT. Lots more weight and lots more frontal area. So, we know we are pushing the capacity of our Trailblazer but we have no intention of towing this combo through mountains. We had our "maiden voyage" last weekend on a 360 mile round trip. I can run 55-58 mph or so just fine with very little shifting going on save for a long hill. Wisconsin is pretty flat and we aren't taking it more than a couple of hundred miles at most.
That said I would NOT want to tow it for long days though mountains. Its the constant shifting that will burn up the transmission, even with an extra cooler. Still you should add an axillary cooler if you haven't already. But I agree with the others, you need something a little beefier to get through those mountains.
bmanning wrote:
Performance is so subjective; some are happy to motor all day at 55mph & 35-40mph in big hills while others will clench their teeth is they slow from 75 to 74 on a climb. Most of us fall in the middle.
This is perhaps one of the best, most balanced comments on towing I have ever read here.