It could be your rear drum or rotors. I posted a while ago about the classic rotor shimmy when braking. I asked if it could be the rear because I did not have steering wheel shake. I didnt get much reply.Hi guys,
I have a vibration/rumbling when i am on the freeway doing between 60-75,it's not my tires. IT's hard to pin point if it the front center or rear,could it be my front hub bearings or drive shaft need to be lube.
When on the highway and you are in a safe area (not many cars, right lane), take your foot off the gas and shift into neutral. If the rumbling goes away it may be tranny related.
Your issue sounds balance related as you mentioned the vibration changed when you switched tires. I found that some tire shops do a poor job with stick on weights.I have recently purchased a 99 LC and I have a vibration in the steering wheel at about 65-70 mph, it had michelin cross terrain tires on it that were getting close to the tread wear bars, so i first had them rebalanced and rotated, it seemed to help a little but the vibration in the steering wheel was still there, so i put on a new set of michelin LTX M/S tires thinking this would eventually solve this problem, but it didnt it seems a little worse now than before. If you figure out what is wrong with yours please post the solution.