First, record the load over time to make sure the breaker is not tripping on an over-current condition, i.e. doing what it's suppose to do.
Most likely, in such a moist environment and electronic trip unit on the main breaker, my thoughts are that the breaker is nuisance tripping from the ground fault feature of the trip unit. Sometimes the moisture gets into the circuit board of the trip unit, shorts out the traces, causing erratic mis-firing/ breaker tripping. Other times, often due to age, the trip unit trips for no reason and needs to be replaced. We have replaced the trip unit of a 4000A breaker (SS trip unit) due to GF miss-fire (GF trip LED indication on the trip unit) and this was a dry environment!
Was there any Trip Light indications (if they exist) on the trip unit when it tripped?
Primary Testing with high current or Secondary Injecting testing with a test set is a waist of money as Ragin Cajun suggested. Testing only tells you that it will trip if the thresholds are exceeded, not that the trip unit
WON'T trip due to it just being defective.
Try raising the GF trip settings (Pickup and Time) to maximum. If it still trips, see if the trip unit is replaceable and replace it with the same or the thermal-magnetic equivalent.
According to this link it is:
https://www.google.com/search?q=cut...MTDABHZ8WDhYQ9QF6BAhIEAE#imgrc=0pICK2rs_JJHxM
If not then replace the breaker.
Lastly, I never liked aluminum cable but changing to copper cables will not stop the tripping and is only a waist of money. The moisture problem has to be addressed and corrected (change enclosure to NEMA 3R ?) otherwise other problems will occur down the road.