How to deal with inrush current tripping circuit breakers?
NTC inrush current limiter, might be an option if you can find one that fits your requirements. The NTC inrush current limiter is a negative thermal coefficient in other words its resistance decreases as it warms up, so this devices limit inrush current by acting a series resistance and as current goes through it warms up and its resistance drops allowing higher currents to go through. You can check more info in wikipedia
Edit:
This previous answer looks like it might be helpful.