How did you verify the amps? Note that a clamp on ammeter can verify the amplitude but not the direction of current. Can you confirm the monitoring doesn't show anything weird for load currents? Both CTs are in the right direction?
All that asked, I'm currently leaning against the CT installation being the issue.
Do you know the response time of the Sol-Ark PCS? How sure are you that it is limiting export to 160A within a second or two after load changes? Does the tripping correspond to instances of high load or fluctuating load?
Your 10-45kW load represents a variance of something like 145A. Supposing 35kW of load dropped all at once, and this happens at the same time the inverters were exporting 160A, you are now export 305A. Or maybe more on one line? If the Sol-Ark response to this isn't faster than the breaker trip time then that could be causing the trips, given you apparently have 375A of total inverter output available.
I also wonder if the breaker trip setting is correct, as someone asked above. A lower actual breaker trip point would exacerbate what I just described.
Is it possible to limit the total output of all inverters to less than 300A (or whatever the breaker trip setting really is) regardless of load and export? That would ensure that the inverters never output enough current to trip the breaker at 300A, even if all 45kW of max load drops at once. If the issue persists after that, I think the breaker is somehow to blame, although I can't explain how if it doesn't have GFP and is otherwise suitable for backfeed.