I think I might be able to answer my own question by rereading your posts from back then.
So I hitch my trailer tongue to the rear of my vehicle. That increases the load on my rear axle. Since I have a WDH, that pushes that weight further down my frame to my front axle, and a little to my trailer axles. Now if I adjust my WDH such that the weight applied to my front axle is the same as prehitched, then the weight is pushed back to my rear axle once again. However, the weight applied to my rear axle can only get as heavy as my front axle before it begins to affect the front axle once again. The weight applied to my rear axle above the weight already placed on the front axle is then forced to the trailer axles...
If I'm not just completely off, then my rear axle weight will increase to 3580 as well. This will result in a GVW of 7160, 60 above my max. The rest of the ~1000 hitch weight will then be added to the trailer axles. So in my theory, I need to have the front axle no more than 3550, use a WDH, and ensure the remaining weight pushed to the trailer doesn't exceed its GVWR, my tow capacity or the combined GVWR...
I'm not really getting into whether the weight is "distributed" or that the WDH is actually applying a separate force. I'm fine if I am technically incorrect if my end notion on how the weight will act against my axles is correct.