If I follow your description correctly, I would suspect the problem to be either with

a) the wire connections to your receptacle (BEFORE you disconnected it and re-attached it - sounds like you have a better connection now), or

b) the receptacle itself.

So if it happens again, try replacing the receptacle with another plain (non-GFCI) receptacle.

If it still trips, then get a new GFCI (and yes, I would get a GFCI receptacle and a regular breaker - cheaper, easier, meets code. You're not protecting the wires, you're protecting yourself or someone else who is handling the motor and plugging it in or unplugging it).