I have an 05 V6 AWD. I've towed about 1800lbs (my 800lb VTX, 300lb XR, on a steel deck single axle). Hills required 2nd with not much throttle to spare. The cooling fans ran a lot with that load, and my trailer wasn't catching much wind. Economy was about 15mpg (vs 24 empty running the same route) on a 600mi round trip. I ran 65 towing on the flats and whatever it could manage on the climbs.
They have a separate trans cooler stock, but it is still going to get hot; you just can't keep the converter locked enough as you add more pedal. Personally, I wouldn't approach 3k if you were wanting to travel very far from home. The stability was there, the drivetrain just isn't up to the task. Ther nice thing about the 3.0L is that it is overbuilt, it is hard to kill. I think a FWD 5spd man trans would make a better tow vehicle.
I sold that trailer and made a really little trailer just to relocate one bike at a time, that was bearable.