The current waveform that is distorted and laden with harmonics isn't just on the load side of the tx. It is present on the source side as well. Its much easier to record and measure on the secondary side because we have a plethora of really good instruments to measure with nowadays.(Fluke comes to mind here)
If you can't get access to the secondary side of the transformer, you are just about sunk. Unless you have some really specialized equipt. and some really good people trained in high voltage work, I'd leave the high voltage side alone. I doesn't make any sense to me why a customer would not allow you access to the secondary side of the transfomer if they are experiencing problems.
Where I work we have a large industrial customer with the same problem. They burn up 1500KVA and 2500 KVA transformers regularly. They don't have any electrical employees and they are NOT willing to listen to our explanation that they are creating their own problems. The effect they have on our 13KV feeder is profound. The substation that feeds this customer is over a mile away and the harmonic content they project out onto the feeder rattles the blocking in a dry 37.5 KVA station power transformer back at our substation! We are currently in a situation with them that I'm not at liberty to discuss.
It seems to me that your efforts may be best directed at getting access to the secondary side of the transformer. Make sure you have proper test equipment at hand in case they finally agree to allow access. You might get only one chance. One thing I wouldn't do is provide a steady stream of replacement transformers. If you are having to eat the tx replacement costs, I'd go the legal route and do what you can to get access to test the load and PQ on the secondaries. If the customer expects you to replace the transformers, you are entitled to know why they are failing.
Lastly, I'd push the PoCo for any information they collected. The fact that they are not willing to work with you tells me a couple of things.
They don't know what the hell they are doing and they don't know for sure if the problem is theirs, so they are playing CYA.
If they had people on board who REALLY understood PQ, it would be likely that they would tout this and in an effort to be a "friend and partner" to the customer, they would be johnny on the spot to help. People who don't know what the hell they are doing tend to hide and do their best to avoid any situation where they may wind up looking like dumbs*#ts. If you don't know what you are doing, it's easy to wind up looking like a dumbs*#t. You'll probably see Hell freeze over too before anyone at the PoCo admits that they don't know beans about hamonics.
2. The PoCo you are dealing with is full of what I call "Ostriches". I have them where I work too.
Any time there is a problem or danger, an ostrich will stick their head in the sand and just stand there hoping that the problem will just go away. I see this foolishness almost every day.
God forbid that someone may actually take the time to set down, read, and learn something about harmonics! Why, that would just take too much effort!
Albert Einstein said he tried to not let his education get in the way of his learning.
In the same vein, just because the power company is in the business of electrical power, don't expect them to know much about it!
(\\..Rant mode off....//)