Problems when driving 55-60 on the highway

I have a 1998 chevy lumina with 233,000 on it. When I drive on the highway and I reach around 55-60 miles per hour, I feel like a "chattering vibration" comming from the front end. If I slightly turn my steering wheel to the right, I can feel it more than if I slightly turn to the left. It almost feels like - your in the far left lane on a highway and you slowly move over to the soft shoulder and you come in contact with the grooved washboard pavement that they place into the road when they repave the highway. I know that sounds wierd but I am trying to give the best description that I can. It is not as pronounced as that example, but it is similiar. I put a new tire on the right side about two months ago and it was around that time that I noticed this vibration thing going on when I drive on the highway. I did have the new tire balanced before they mounted it. I also had a front end allignment around the same time and the mechanic never mentioned anything he found bad so I presume my front end is sound. I am not sure if it's my steering, my transmission, or something else. It is so hard to find an honest, reputeable, mechanic where I live. They all want to replace the entire vehicle instead of just fixing the problem. Any assistance regarding this matter will be greatly appreciated and it will take me in the proper direction in getting this thing fixed. Thanks!!!