I put a 2.5 lift on mine w/ 31's and did the very same. This is what I have done and learned.
Do not rotate your tires!!!!
Check all your bushing for wear track bar, steering stabilizer etc. Replace if needed.
Tighten ALL bolts on the steering and track bar components. Some people will say to torque but I just got up on em, but either way.
Re-grease all your ball joints.
Play with tire pressure, to much or to little in conjunction with other symptoms with come in to play. I run 31's psi Max is 44 so I'll go 4-5 lbs lower.
This is obviously after you do the alignment and balance.
These are the step I took to rid the DW but remember It could be a combination of things so It will be hard to isolate that's why there's a grocery list. I also repeat these steps after I've gone out three or four times OR if I feel a "shimmy".
REMEMBER these are steps I've taken that has worked for me and the info I have obtained was from the good people of WF and my local off road shops.
Good luck my friend!