Semi tractor vibration/shake

Based on what you've written, I would look at injectors. I would also consider a new damper and add a balancer while at it.

 

Check your ride height.
A wrong ride height can cause an out of spec pinion angle or can just change your driveline balance by changing one u-joint angle.

 

I've had the shake about 4 times over last few years, and every time it's been a tire, usually on the trailer. Granted mine is a four axle trailer and it's usually on the steerable tag axle. But always when loaded at around 45 mph. Visual inspection of tires and air pressures were normal.... After checking everything else we replaced the tires and shake went away. That's been on brand new steers with only 5000 miles, a passenger side tire on the tractors drop push axle, the tag axle I mentioned on trailer 2 time (one time each side)..... In all cases tread, air pressures, rims, etc all looked fine. But every time it's been a tire for me.

 

And a super short wheel base exacerbates the issue.

 

I am a fan of the balance beads, but also know that they can cause as many issues as they solve. I once installed them on a pair of tires that had no balance issues, thinking that it cant hurt, it would just be a preventative maintenance thing for tire wear. Wrong. Even with the proper weight of beads for tire size, because the tires were already "perfect", the beads had no where to scramble to. At 60 the truck developed that ol' out of balance tire shake......