FOG1: Deep breath. I know this is frustrating, but try to remember that this is a free public forum, and that the folk rubbing your the wrong way are trying to help.
GAR is a fantastic theory guy. He tells everyone that they need to understand more theory. His scope pictures are great if you want to understand the root cause of transformer inrush.
Back to your problem: there is clearly some factor that you don't know is important to describe, that the electricians involved haven't sussed out, and you are hoping that someone here can figure it out. The practical electricians here will give you things to check. The theory guys (myself included) will want you to make measurements.
This thread is long and months old, and most of us don't have our noses in the issue and will have forgotten details.
Could you repost details such as the system voltage and configuration (480V? Wye, delta, grounded, etc.?) Transformer rating and nameplate, pictures of the transformer connection. Is there any other equipment around which seems to affect the transformer operation?
The fact that the transformer no load current is so high makes me think that it is defective. You said that the supplier confirmed that the first one was defective, and it would seem hugely unlikely that the second one is defective. So while it is possible that both were defective I guess we are now looking for common causes that could cause the same symptoms in perfectly fine transformers.
You could have:
Too high voltage for the transformer as connected (are the primary voltage taps correct)
You could have a misapplied transformer (very common when transformers are used in reverse)
You could have unbalanced supply voltage (maybe there is a wiring fault upstream)
You could have high harmonic voltages present on your service.
Something could be injecting DC current into the circuit.
Something external to the transformer could be injecting a large DC magnetic flux into the core.
When you said that the prior transformer was defective, what tests determined this, and where were the tests run?
That's it for my Sunday morning thoughts.
Jon