Engine/drivetrain vibration?
Something doesn't sound right with the balance job. If the invoice says it was balanced, but the converter with weights was for a different application, it couldn't be right. You can make the rods and pistons all weigh the same. But the crank still needs to be put on a machine & spun to get its counterweights right.
Someone should have a part # for the new converter to confirm what the original application was. If it was for a 360, it had too much weight for a cast crank 340. If all of the weight was taken off, that's not correct either because it needs a little, but less than a 360.
Ask the machine shop what they did to the crank to balance it. The only ways I know how they could have correctly balanced it would be if they added mallory metal to the rear crank counterweight, used a B&M plate or used the old, original converter. Not sure if they can figure the extra weight needed to simulate the converter or flexplate counterweight when they spin the crank without actually having one bolted to the back.
I'm not up on the details of actual machine shop work, but I believe a balance job basically works like this:
* All rods & pistons are machined to weigh the same. Rings, rod bearings, pins & locks are added into a formula.
* Weights representing the formula totals are attached to the crank to simulate the rotating assembly and the crank is spun.
* The resulting balance machine readings tell the operator where and how much the assembly; crank (balancer and flexplate/converter if installed), are off from optimum.
* Weight is then added or removed from the crankshaft counterweights to balance the assembly. It can take several "spins" and machining to get any unbalance minimized.
It is a good practice to have the correct balancer and flexplate/converter, that are to be used, bolted on the ends for greater accuracy. They MUST be bolted on, or weight compensated somehow, if you will be using counterweighted units, like in a cast crank 340 or 360 application.