Boat lift motors and GFCI trips on startup — moisture is the usual suspect, and you're already thinking along the right lines. But rather than just running it to dry out, megger the windings phase-to-ground. That will tell you in thirty seconds whether the insulation is breaking down. Anything under a megohm on a small motor like that and you've found your leakage path; running it hot might dry it out temporarily, but deteriorated insulation only gets worse.
Check the terminal box first — it's the most common water entry point, and corroded connections in there will leak to ground on startup when everything's cold and damp. Also have a look at the start switch area while you're in there.
The capacitor theory is a red herring for the GFCI part: a bad start cap keeps the motor in locked-rotor longer, which is an overcurrent issue, not a ground fault. The GFCI is seeing real leakage to ground — the video of it tripping right at startup is classic winding/terminal-box moisture.
And completely agree on keeping the GFCI in the circuit. On a boat lift, "you bet your life" is exactly right — never bypass it to get through the season.
