It appears pretty simple to me, but I've encounter this situation many times. Customer acquires a machine built for a voltage other that what they have. They want to use a transformer they have , or buy a used one for cheap, and connect it in reverse. I've seen many do it. They don't realize that the output coil is nearly always a delta coil, and there is no simple way to ground it, other than corner ground it, or leave it ungrounded. Neither do they realize what the implications are of leaving it ungrounded and floating or corner grounding it. From a safety aspect or equipment operational problems or damage that may result from doing so.
A lot of equipment today built as standard, doesn't play nice with an ungrounded or corner grounded supply. Most new equipment with any electronic requires a grounded wye supply to be reliable. Codes and listings aside, if I'm going to do it and accept the liability and support for the equipment, I want it done right. No mater what the buyer, salesman, line assembler, engineer or inspector thinks. I understand the difference and make it proper or I walk.
It seems clear in this case that the vendor selling the equipment, supplied the wrong transformer, and doesn't understand the difference. The machine builder clearly built the thing for a 480V grounded wye, and the machine dealer cobbled on the wrong type transformer to make the sale. And the customers contractor doesn't understand either.
The codes and standards are not a how to manual or a design manual and should not be used as a substitute for knowledge about the system engineering and design. Nor should they be used as a workaround, to get past inspectors, engineers or designers that aren't fully up to speed with the situation at hand.
This job needs the correct transformer, bonded and grounded properly, and that can't happen with what the vendor supplied. Simple.