Adding to Bjarney's posted information, I have a few Q's / comments / etc.
[*]As to the high load amperes recorded, how long was the duration? Does the current stay steady thruout the complete surge time duration?
[*]Is there a corresponding load amperes increase on the secondary side, or at the subpanels, during this surge period?
[*]Do you have an equal 100/3 or 125/3 frame to swap with the existing breaker, while you shoot trouble on this situation?
[*]Have you examined the Transformer Coils for signs of arc faults? Have you checked the Branch Circuit and Conduit feeding the Transformer completely for other barbequed insulation?
[*]Can you smell fried Varnish or essence of barbequed thermoplastic insulation?
I am leaning towards an Arc fault possibility - either in the transformer enclosure (Coil/s to Core or Coil to Coil, also the branch circuit conductors terminating at the lugs), or somewhere inside the conduit feeding the transformer.
If the surges are corresponding to draws on the secondary side, then ace the arc fault ideas!
Maybe you should Megger the transformer's coils, to see if you find leaks. Also Megger the branch circuit feeding the transformer.
Really sounds like an Arc Fault, but maybe the 100/3 breaker is toasted from the excessive heat concentration of the loose termination lug - that barbequed conductor may have also been a result of an arc fault, but more likely the loose connection under a steady high load heated the heck out of everything available, and the copper wire did it's normal heat sinking action! (and the breaker became the slave sink!!!)
Let us know the outcome!