Inrush is something we have always had to deal with, especially with motors that are direct on the line start. The inrush can be as high as seven times the nameplate current. The damage created can be minimal if the motor is started up in the morning and them runs all day. A motor that runs on a variable frequency drive can be subjected to the same level of voltage spike all day long. The transients are so bad that the conductor we used in electric motors was no longer good enough.

1) Your Breaker or Motor Circuit Protector Rating. What is AT rating of that breaker. That must be covering your full load capacity of Motor.
2) The motor is tripping due to overload. I think overload relay setting should be checked. As a thumb rule, this relay shall be set between 15 to 20% of motor full load current. Check manufacturer's recommendations for required settings.
3) if the trip appears at the motor start phase the soft start can be failed, because it should reduce the current to the limit value.
4) if the trip appears when the soft starter is bypassed then the motor is mechanically overloaded.
5) Check the soft starter settings. There should be ramp up time of 10 sec and initial voltage to be 40%.

You will do better by focusing on the efficiency of your equipment how it is operated and the maintenance of your equipment than trying to tweak your pf by .03. But if you decide to install a capacitor bank anyway, you need to talk with your utility and make sure you do not cause any harmonic resonance and get them to help you with what your ROI will be. By the way, you may also have to install line reactors at each soft starter (and at all VFD locations) if you do not already have them.

Indeed, it's better to have a soft start system. This is modern power electronic technology to start the motors. The selection of starters depends on many factors like motor rating, voltage rating, application of motor, the running sequence, protection and control. You would require approaching the soft starter manufacturers with all details and they can advise you the best solution.