I did the same thing last month, but with a 3.6L JLU, because my TJ's axle gears had eaten themselves 2 weeks earlier and I haven't had them fixed yet. I was in the same area, with elevation ranging from 10k to 12,900. It's an area I wheel in at least once a year, including the 2 week previous trip, so I'm familiar with how my TJ performs in that terrain and elevation.
Crawling is a rare area where my 4.0/AX15 feels like it has all the power/torque I want, in immediate supply. I was surprised that on steep inclines, even in low range, the 3.6 really bogged down and felt pretty gutless compared to my 4.0, requiring a LOT of extra throttle to not lose speed.
I also didn't like that on the steep downhills, there was a point in the rpm where it seemed like engine braking would let go. I'd be letting it crawl me down and suddenly it would start accelerating without any throttle input. I don't know if that's normal for an automatic or what but I didn't like it one bit when I'm crawling down toward the hairpin in a switchback with a thousand foot drop on the other side.