Let's look at the information that we have.
All motors exhibit a current unbalance.
I understand that all the plants on the same circuit show the same problem.
There is a 2% voltage unbalance.
One substation transformer runs disproportionately hot.
There are voltage adjusting tap changers in the system.
Most likely cause; The tap changer on one transformer is one tap out of step with the others.
Second choice; The primary supply to the substation has an unbalanced voltage.
Third choice; Both of the above. The incoming voltage is unbalanced and a tap changer is trying to correct and causing or worsening a phase shift.
In regards to the ammeter readings. It is common for the reading on the center cable of three parallel cables to be influenced by the other two phases being in contact with the outside of the tong of the clip-on meter. Most experienced electricians and technitions are aware of this and recognize the effect and try different meter positions until they get a reasonably accurate reading.
You may want to try switching the ground to another corner of the deltas to rule out any weird one-in-a-million high resistance ground faults that may be causing problems.
Do you have one transformer in each bank that is much hotter or much cooler than the others?
Are you able to do any trouble shooting at the plant?
Specifically, during the weekend, or slow period, is it possible to kill the transformer bank long enough to change the tap setting on one of the transformers?
I would not normally suggest running banked transformers on different taps. In this instance it may be justified as a trouble shooting measure. If you can mitigate some of the problem with an off voltage setting of a transformer tap, you may make a strong suggestion to the utility that they have a voltage problem and should check their tap changer.
If you are able to improve the situation by changing a tap, it is up to your judgement whether to run that way or return the tap to the original position and wait for the utility to respond. If you choose to run one transformer on a different tap setting, please co-ordinate with the utility and restore the setting immediately the utility completes repairs or adjustments.
Running your transformer banks on different taps will be treating the symtom rather than the cause, and may well mask the problem at the substation. The utility may then want to think that the problem has healed itself and never check their equipment. Your call.
respectfully