If the Overload Relay is tripping, it’s not a bad coil, aux relay, etc., an OL trips because the current is too high. Plain and simple.
Did you check the current in all 3 legs to make sure they are balanced? IEC and Solid State OL relays will skew the trip point to be lower than the setting if there is a phase loss. So even if the current in one or two of the phases is “normal”, it can still trip if there is no or low current in the 3rd phase.
Another possibility is that your control signal that engages the starter is chattering, making the motor starter bounce on-off-on-off-on-off really fast. That causes the current heating effect in the IL relay to trip it off line even though when you read it at steady state, it appears normal.
Another possibility is that vibration has worn away the insulation in the motor connection box and occasionally the mechanical movement in the motor causes it to short to ground, but in a high resistance manner that is not causing the breaker to trip first.
Bottom line, this needs sone expert troubleshooting based on starting with what you KNOW moving toward what you don’t know.
" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden