"Next, look at the tongue weight on that trailer and the gvw; 14k gvw; tongue weight 1560 minimum (will be more like 1800-2000 fully loaded)."
Ramit - I was off in the above statement. I added the weights from the Keystone website in my head and somehow came up with 14k instead of 13k - the joys of getting senile
The 1560 is 12% of the 13k gvw which is the least I would think you would want on the hitch (fully loaded) but probably doable (depending on how it tows loaded). At that minimum weight it only leaves you about 900 lbs. for people and stuff before exceeding the payload. With a toyhauler, the toys and all the paraphernalia associated with them that you will want to carry it will probably be difficult to stay within that number - I could be wrong but it is SO easy to have so much required "stuff" that 1000 lbs. would be EASY to hit - especially when including people. Just keep an eye on those weights (scale).
Yes, the Equalizer maxes at 14k as far as I know and 1400 on the bars. I am not familiar with the Blue Ox but if they give you higher alternatives sounds like that's the way to go. As I mentioned, something is wrong with the setup by looking at the pic. When I went to the HD truck I had to get an extended shank for my Equalizer because my trailer sat with the nose in the air. The truck did not squat like yours, but the shank was definitely too short. You may have that issue as well.
As far as the squat, I'm having a hard time figuring that out. It IS an HD truck as mine is. Mine is gas and has a payload of almost 3200 lbs. with about 1200 on the hitch. When hooking up without the WDH it barely drops (it sits tail high - no leveling kit and drops to just about level with trailer on) and looks nothing like yours. Reckon the leveling kit has transferred too much weight to the back causing the droop? Did the mod somehow change the dynamics of the OEM suspension and weaken it as far as towing ability (I can't imagine how)? That situation warrants additional research and inspection. Hope you can get that fixed.
I also hope you get the stairs. Sounds like you are about to go through the dreaded "do I have a good dealer or not" scenario. I wish you luck on that and getting the AC problem resolved.