My truck has close to zero, if any, frame movement when steering lock to lock, stopped on level ground, as shown in the pics.
I do have the ORD steering box brace installed, and no sway bar.
Im thinking maybe your springs are softer than mine causing the frame to tilt, my springs are very stiff and its a fairly harsh ride. Ultimately your springs must compress on one side for the truck to tilt so i think it must be the springs....or maybe bushings?? Maybe you have rubber spring bushings, i have poly, i think most lift springs are using the poly bushings though....
Seems a shame that it wont pass inspection that way i would think it would lend to better axle articulation off road that way.
We dont have inspection in CA, just smog test, they dont care if our vehicles are safe to drive or not as long as they run clean lol.
There must be some way to firm up that ride to pass the inspection though.....