Hey Scardup, the rig in the middle in the pic below is mine. 2012, 3.6, auto, 37s, 5.13s. The trailer, loaded would go ~2k or maybe heavier I'd guess. The data plate says 1250 empty, + the shell, rack, 10 gal. Fuel, 10 gal. Water, spare parts, and all my camping stuff.
That pic below is on our way back from Dinkey Creek Campground near Shaver Lake (east of Fresno, if you're not familiar). CA 168 on the way up to Shaver has a grade that will tell you how your rig is set up for towing. It's 9.4 miles long and gains over 3000 feet in elevation. Average
grade is over 6%. There are signs warning drivers to turn off the A/C, several places to get off the highway, and a couple of water tanks on the way up for those who have overheated. Not in my Jeep, but in my Chevy Colorado, I've actually turned on the heater to try and get some more heat out of the coolant. (Nothing like scalding your ankles in July.)
When I was on the way up that grade I pulled down to about 35 MPH just to hold the temp down on the engine and especially the tranny. They still got hotter than I was really comfortable with. (Should've taken a pic because now I can't remember the exact numbers but the tranny never got to 200 -- 195 though, I think.) The 3.6 had plenty of guts and I could've kept my foot in it and held 55 -- just didn't feel like killing it to prove a point.
I think you'd find the 3.6 has the guts -- when set up correctly -- to handle what you described (plus a lot more), with no trouble at all. But the guts are obviously not the only limitation. Now, to contrast with my experience going to Shaver lake -- last year I took basically the same setup to Sierra Trek and held 65 all the way up 80 to Truckee with no heating issues. And I've used the trailer for a few trips to Reno helping my daughter move stuff in and out of UNR and never had a hiccup. That grade up to Shaver is just brutal, and it's notorious for eating rigs' lunch.
Bottom line is that I think you'd be happier with the 3.6 than your 3.8, but depending on where you want to pull your trailer to, you may still find that you have to baby it occasionally.
BTW, I used to see you in Livermore now and then (before I was on here), but haven't in a long time. Always loved the tag.
All the best.