To weigh in on the whole shutting down the transformer thing. Unless I knew we were going to be down for a while I would not open the breaker feeding the xfmr.
Magnetizing inrush on a transformer can be somewhat random as well.
I think without any details of the electrical installation on board, it’s ALMOST pointless even discussing potential causes. We have so little information. It is fun though.
I did just have a very similar fault though. Relay was never commissioned properly. many possibilities.