There are two major factors that go into the reduced towing capacity of the "non-big-tow" Armadas: The gear ratio and the rear suspension support.
First, let's talk about the gear ratio. The reason this is important is because of the torque that must be applied to the driveline in order to generate force at the pavement. The lower the gear ratio in the rear end, the greater the torque must be in order to generate the same force. So, if you look at the 2.94 vs. the 3.36 ratios, the former is going to require approximately 14% more torque at the transmission output, on the drive shaft and universal joints, and the input to the differential, to maintain the same pulling/driving force. These higher stresses require a reduction in the tow rating of the vehicle in order to prevent breaking things.
Second, let's talk about rear suspension. The rear springs have a particular spring rate (k) that is expressed in terms of force per unit displacement. In other words, so many pounds of force per inch of displacement. In order to tow safely, you must still have adequate suspension travel at the rated tongue weight. The addition of the airbags effectively increases (k) so that more force can be placed on the spring for the same displacement. This increases effective tongue carrying capability and maximum tongue weight.
With adequate aftermarket parts it is possible to achieve an improvement in tongue weight capability (even though doing so does not change what you can legally tow without recertification). It'll still drive a whole lot better with a higher effective spring rate even at moderate tongue weights. Similar improvements can be seen by using a weight distribution hitch, which you should always use if your trailer exceeds about half the weight of the tow vehicle or half the tow rating weight, whichever is less.
So, in short, here are the takeaways, bearing in mind that IANAL:
1) There is nothing you can do to your car with aftermarket parts to increase the legal tow rating of your Armada. If you are in an accident and are towing more than the nameplate tow rating, I believe you would be excoriated in civil court regardless of what you might have done to mitigate it. IANAL and YMMV, but my personal feeling is that I would never take that risk, even though I am sure people do it all the time.
2) That said, you can use common sense when determining the mechanical capability of your vehicle to tow a particular trailer load. The SAE J2807 tow rating test is harsh. If you are pulling on flat, level ground or mild grades, you can use that to determine a lower level of mechanical stress on your drivetrain, compared to the 5.5% average grade used in the SAE certification test. Accelerate slowly, climb gingerly, and just hope your u-joints don't break.
Last comment: I would not tow more than the nameplate tow rating, and just enjoy the better ride that aftermarket airbags and a WD hitch provide.
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