AVK Alternator - Aux Winding Problem

Measure the voltage and amperage needed by either of the 2 operating gensets, and on the failed set either tap the main output windings, add a transformer, or a separate power supply off of the other gensets.

Instead of a transformer, could this person add a PMG instead?

I would think it would be more cost effective to rewind the auxiliary winding, unless the PMG is offered as an option on the generator its mounting would be quite a project and take considerable time. The power for a voltage regulator with separate sensing doesn't need to be all that precise so a off the shelf power transformer would be a quick and low cost alternative, a major repair could be done at a scheduled shut down.

Not having a full circuit diagram of the AVR + Power sharing information, it will be very difficult to advice on how to do an alternative supply to the AVR:

You said that the 2 aux windings each of them is wired to the AVR. Having this configuration suggests to me that the aux supplies (you are mentioning) have a different or an additional role to play in detecting the alternator's status in view to adjust the voltage and do the sharing of reactive power. (just awarning that just supplying from a different source might not solve your problem... may be worse off?).