I don't want to be some hillbilly who bypasses safety equipment but I'm telling you, GFCIs have been a pain in my ass more than once. I encountered a similar problem - GFCI in a bedroom - removed it and everything worked fine, no shocks coming from anything.

I'm gathering on the web that some older style motors have a tendency to trip GFCIs. This pump moves water really well, I don't know how long the electric seals last or how old the pump is.

The best route would be to replace it but damn, it's in an awkward spot.

I'm curious about grounding though. I know the green or bare grounding wire goes on to the neutral bar in the box but isn't that attached to a long rod driven into the ground? It seems like groundwater would dissipate the charge deeper than one of those rods. During the rainy season, those rods are in steady contact with ground water. So if there was a ground fault in the pump while it's submerged in groundwater, it would almost be the same as if you touched hot to ground, which would trip the breaker. But I don't really think it works that way, I'm not sure why but I think it's because water is not an ideal conductor.

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1986 300SDL, 362K
1984 300D, 138K