Assuming it can be distributed between the two BMS evenly, it might be fine. Of course, that depends on if the BMS can handle its rated current. They also have a surge current, but it's likely a much shorter duration.
I also don't know that I'd trust that the peak is only 235.8A since a meter NOT in inrush mode likely won't capture the inrush peak with the MAX function, and I don't know if the inrush function in AC mode would capture the peak current either.
The inrush on a motor is typically 4-10X the run current, so my gut says the low end of your actual peak current is > 300A based on a running current of about 77A. I wouldn't expect the BMSs to handle it.