Our tune up guy was handed a brand new Caprice off the lot to fix after they discovered it wouldn't start. It was back in the early 80's right after GM started putting ECM computers in the cars. It was a v-6 and he discovered that it was only firing the plugs on the left bank cylinders. The right bank was totally dead. He scratched his head over that one all day. Replaced the chip twice, then replaced the ECM, again, twice and it still wouldn't run. I finally suggested that he go get another identical unit off the lot and switch the ECM's. Both ran perfectly.
Slap on the FM sticker and get them out of here.
I'm still researching your problem, Webster. I didn't forget about you.
So far, I've only found one reply from an alleged GM certified master mechanic who suggests that a .033 shim needs to be placed under the motor mount on the drivers side. It is possible that normal engine vibrations could be transferred into the frame. That mount is very close to the steering connector shaft. If it hits harmonic resonance at the speeds you've indicated, coupled with road conditions, it's very possible for it to be felt a little in the steering wheel and more so through the rest of the chassis.