If the trailer is 38xx lbs and the tongue weight is 320 lbs, then the trailer only has an 8.4% front bias, its suppose to have between 10%-15% forward bias, so the trailer isn't loaded properly and that will affect control of the trailer and safety....
It the trailer is properly loaded, the tongue weight will be at least 38x lbs...
More than 350 lbs tongue weight you should use a WDH.....
If you have to charge a battery on the trailer, as well, electric trailer brakes, the Tow Package has a greater alternator capacity to supply electric power to the trailer...
The 2011 O.M. says in a not so direct way, the limit for non-Tow Package equipped vehicles is 3500 lbs.....
As we've been discussing, the Tow Package has nothing in it to help you control the tow load... ...the Load Leveling doesn't help you control the tow load, if anything it might make the weight distribution just slightly worse, it just levels the vehicle for convenience....
The rest of the items on the Tow Package are for protecting the vehicle against the stress of pulling the tow load, to include bigger alternator and a full sized spare... ....so if you try to tow at the max limit for the vehicle with the Tow Package, provided you use the required WDH, you probably won't have any problem with handling the tow load, but you may damage the vehicle from the stress....
If you install a Tow Hitch in WK2, this trailer is a couple hundred pounds above what you can just hook up to the hitch and drive away.....
And I suspect that is why they set the non-Tow Package limit at 3500 lbs, its the max weight you can hook up and drive away without the extras, like a WDH...
So I can't say, Oh yea, you can tow more than the O.M. capacity, but if you're only 10% over (considering the vehicle can safely controls load almost double that, but it would overstress the engine/electrics) do it properly I can't see you having any serious problems... ...unless you get a flat and only have the undersized emergency spare, then your stuck...
But that means you have to do it right and use the right safety equipment, Make sure the trailer has the proper weight distribution, get a WDH and set up electric brakes....
Make sure your cooling system is in good shape....
The biggest problem you might have is the standard capacity alternator... ...check your build sheet, it will say what size alternator your vehicle got at the factory.... ...I replaced my alternator in an hour with simple hand tools, so that is always an option, get a rebuilt 220 amp alternator and swap it in, but a good rebuild of an alternator, especially the higher capacity will be several hundred dollars, if not $400... ...having a voltmeter and learning what it is telling you, could help, you can always get something that plugs into the cigaret lighter... ...take the trailer out for a series of longer and longer test drives to test it out and make sure it works and you're not dragging down the electric system to discharge your battery's....
I'd defer to Jim or anyone with more towing experience than I have.... ...one thing I am confident on, you're trailer is just over the "Install a hitch, hook it up and go", you need to get the safety equipment (WDH, electric brakes, full sized spare would be smart also) and make sure your electric system can handle the trailer...