Took me a while to read everything, but I agree with you (Jdrais) that this is a problem on the UTILITY side. I have come up against this sort of thing several times over the years and unfortunately, I can tell you that you are going to be into a fight with them. The upshot of each situation I have been involved in is that the ANSI regs that they spout are true, and yet incomplete, because as you suspect, they ONLY address voltage imbalance. This ASS-U-Me(s) that if the voltage is balanced, the current will be relatively balanced, so from a design spec standpoint, it SHOULD work. So there are no standards for current balance, because current is DRAWN by the user, not PUSHED by the utility. But these ANSI standards were developed BEFORE we had large power electronic devices like VFDs that can draw lots of current in ways that do NOT follow the rules.
VFDs draw current from the line in "chunks" only at the TOP of the sine waves, which is why we refer to it as "non-linear" current draw. Diodes have what's called a "forward conduction voltage" threshold, so they only conduct when the sine wave increases to that level, then ceases to conduct when the sine wave drops. If you have a properly designed system and fully healthy transformers, that is somewhat irrelevant, but when you have old failing equipment, it looms large. What utilities do, and NEVER admit to, is to "boost" the voltage with line capacitors. This is basically a way for them to satisfy the ANSI specifications without having to spend a lot of money replacing a bad transformer somewhere just for one customer. Is this a "cheat"? Some think it is, hence the utilities not wanting to EVER admit it. But the problem then with VFDs is that because of the non-linear current draw, they suck all of the energy from those boost capacitors instantly at the first point of forward conduction (how a diode works) and the voltage drops on that phase to where the next diode on the VFD front end fails to conduct. That then causes a large DC bus ripple, which is what the VFD is actually concerned with, and it shuts down. But when you measure VOLTAGE on that line, it APPEARS normal because the meter is averaging the voltage (RMS), thus allowing the utility to claim they are meeting the ANSI specs. If you could look at it with a high speed scope, you could probably see the issue more clearly. But from the things you describe and the troubleshooting you have already done, this is exactly what it sounds like to me, because I have been there.
In one fight I got into with the utility near Las Vegas, the plant was far out in the desert and the powerlines ran along the only road going there. So on my way to the site for the 4th time to meet with the owner and utility reps, I photographed the capacitors on their pole and when they again denied they existed, I showed them the photo. That was the final blow, they admitted to it then (claiming they were unaware) and paid for the damage they had caused (blowing up some large Toshiba VFDs).