What type of exhaust are you running off of this 350? I also have a 350 s.b. in my 85GMC and right about 1950-2000RPMs the muffler produces a perfect tone that makes everything inside rattle. I am running Flowmaster Muffler. I have also heard the same noise from a 84 Camero at 1900RPMs. Its a vibration that makes everything inside my cab rattle. I'm sure if you have a loud enough muffler it does this. Also at 55-60 it feels like my front end rattles. I am running 31 10.50 All Terrains and upon enquiring wierd rattle to a mechanice we figured out the lugnuts at that speed are expanding because any speed above or below that it doesnt happen. Same with the muffler a hair above or below 2000RPMs and it goes away. Hope this helps!
Now then, does it vibrate when you are not moving as well? If it does, then it is not a U-joint. If it always vibrates at around 2000 rpms, check out the harmonic balancer. If this is bad, loose or anything other then perfect, you will get a vibration. Let me know.
The center support bearing was realy bad in my 81 burb.
After replacing it the vibration was worse than ever.
I put it up on jack stands and had a buddy run it slowly to 55mph.
The shaft looked like a jump rope.
$35 to have the rear shaft balanced and $15 to straighten.
Also, don't forget to check the other end of the engine: flexplate/torque convertor or flywheel/clutch combo. Again, problems in this area will be apparent whether you're sitting in the driveway or running down the road.