The Ram should be fine. A tradesman or express should have plenty of payload. My express has 1478 SLT or above you need to look close.
I don't understand it only having a bumper hitch, unless it was a rental and the hitch removed by the leasing company. It should have the double wire harness plug.
Now Hemis are sold as having "Heavy Duty Transmission Cooling". According to a Ram Tech I talked to it is supposed to suffice with out an aux cooler. Of course he does not warranty my tranny so is his word any better than anyone elses? I have seen temps as high as, 190, on a very steep 1rst gear off road climb. While towing on the road the tranny runs hotter than I like in the 170 to 180 ram tech said that was ok,but then again?
I tow a hybrid with a gross weight of just under 500 lb.