I had the same issue a few weeks back on my 05 Tahoe, I noticed that you have 20" tires on your ride as well. I found that my Bridgestone tires which have around 20,000 miles had 36 psi of air pressure in each tire so I lowered them down to 32 psi and re-set the TPMS sensors. I then drove it to get the tires warm and came back and checked the tire pressure again which showed 34 psi on three of the wheels and 33 on the other so I adjusted the one wheel up tp 34 psi and re-set the TPMS sensors one more time .
The DIC shows 32 psi when the tires are cold, and usually 2 psi per wheel higher after it is driven a few miles. The difference between the 36 psi and 32 psi tire pressure solved the problem I had with the steering wheel shimmy, 32 psi is what I would suggest setting your tire pressures on and give it a try. The balance on each wheel needs to have the weights placed on the inside, and outside of the rim to get a good balance, if you have custome wheels I would have the stick on weights placed as close to the center of the wheel as possible, if the wheel is still way off balance have the tire shop dismount the tire and spin it a half turn from the valve stem and re-balance it again.