Regarding the wheels: If I was going on a one-way trip, I'd put the stockies on and cargo the steelies (you'd be cargoing the stockies anyway, right?). Put the wear/tear on the stockies.
You should be fine towing the 6X12, even if you load it up to max weight. You'd be better off with a 6X12 (GTW4400lbs) loaded with 3000lbs of junk, than you would be with a 5X10 (GTW2800lbs) loaded with 3000lbs. You're better off underloading the larger trailer than overloading the smaller one.
Make sure you get the right hitch drop to keep the Uhaul trailer level. With your lift, you might need a 2" drop (or more). The key is that you want the trailer to be level. This is pretty important and can make the different between an enjoyable excursion and a complete nightmare.
When you load the trailer, balance the load from side to side. Don't load all your boxes of magazines and books on one side and then stack the other side with stuffed animals.
Balance front to back as well. You want a bit more weight in front of the axles than behind (which gives you tongue weight), which is why the trailer's axle will probably be further to the rear. Load it evenly side to side and front to back.
Weigh the trailer if you have access to a vehicle scale.
Whether you can or can't weigh the trailer, definitely get the tongue weight and make sure it doesn't exceed your max before you head out. You said you have the tow pkg, so I assume you have the Mopar hitch receiver. This receiver is Class III and most of your ball-mounts will have a max tongue weight of 500lbs.
You can get your tongue weight with a bathroom scale. Just set a box on the scale and prop the trailer's tongue on the box. It's usually about 10-15% of the trailer's gross weight (if your loaded trailer weighs 3000lbs then your tongue weight will most likely be 300-450lbs). If your trailer's tongue weight exceeds your bathroom scale (which your's probably will unless you have a BIG scale), you can calculate it using this little handy dandy diagram of how to calculate tongue weight.
There are some great tips over at etrailer.com (click here to see them).
Good luck and be safe out there.