Same problem here , probably need and alignment with your new tire..Mine is doing that too after some mile with the leveling kit...

 

Had three alignments already, two sets of rims, two sets of tires to try and figure it out.
Got my front end checked over twice, truck is 100% good apparently.
Going to get some extended Sway bar links to try it out.

 

Did you find a tire store that has a HUNTER ROAD FORCE BALANCE MACHINE ??
That is where i had to go to get my shaking taken care of

http://www.gsp9700.com/search/findgsp9700.cfm

 

Where did you get your allignment? I bet they only adjusted your tow and didn't even bother with the camber. If so, I would go to the dealer to get it done. I had the same problem with my steering, was fine after proper allignment.

 

I had it done at dodge who also have the only Hunter Balancing system in my area. I got both sets of tires balanced from them and still the same issue.
I know the tires are heavy as hell so like you guys are saying it might play a part in it.
Ive spend over $800 in alignments and balancing tires so that was enough of that.
Ride her I guess..

 

Find out that my front tire as wear unevealy on mine i have install my new tire and planning to take it to an alignment shop just like chickenhole said im pretty sure the camber is off , the truck as been realigned right after the lift kit install but i bet the guys never ajust the camber...

 

if alignment doesn't work, i would check ball joints and tie rod ends as well as your steering dampener.