While in there with the shims, replace the rubber trans mount too. If it's original, and these vibrations have been happening for a long while, I'm sure it's shot. That alone could cause problems.
Back in the day when I did 3.42 gears on my 9C1, I got bad vibrations above a certain speed. I tried to have it balanced, but was told it would never work well for higher gear ratios due to its length, resonance and interaction with the B-Body chassis. I had also read that's why the Impala SS is speed limited to around 154 MPH (I think that was mentioned in the ISS Technical Archives). I'll see if I can find a link. 3.73 gears could hit a harmonic at a lower speed.
Anyways, since the early days, the recommendation has always been something that's not steel. Wayyy back in the day, I got in on a group purchase for an aluminum MMC version which solved the problem and I never looked back. The company at the time sold two versions. A stock length and one that was slightly longer (3/4"???) if you wanted to center your axle with new control arms.
This is what scares me. But he asked all the right questions about the vehicle, tire size, transmission, HP, etc. He came highly recommended from several people I know. Tried using local because of previous issues with a out of state driveshaft company
But I’ve done the calculations on critical speed and even had a math wiz double check it. It checks out for length and the two materials I think he used.
I didn’t go with aluminum because I had one in the past from the “driveshaft shop” for a 5th gen camaro and it vibrated at certain speeds. It’s a long story but that’s the main reason.
Edit: it may also be a good idea to check everything again. Check the output shaft of the trans. Bushing wear, etc. Vibrations have a way of wearing things out quickly. I completely grenaded a tail housing on an old Mopar in short time because I ignored the vibrations too long. The trans shop told me the yoke bushing was no longer a bushing. LOL. I still have the tail housing as a spectacular catastrophic failure trophy. And a lesson not to ignore these things.