Yes, Texas, you missed something.
The OP needs to run a ground wire between the panels. This wire would be a "EGC," or EQUIPMENT grounding conductor.
The OP suggests that he instead run a separate wire to his well. This would be a "GEC," or grounding ELECTRODE conductor. Different wire, different purpose.
The OP's idea fails, as 'grounding' the panel to the well will do nothing to help fault current return to the PoCo transformer. He is confusing the electrical 'ground' with the earth under his feet.
Technically it would... with much higher ground impedance than usually and it wouldn't comply with the NEC.
I think I missed to clarify one point: I never actually considered the OPs suggestion to run a GEC to the well, I always suggested running an EGC to the main panel in order to avoid scrapping the old cable. Might not work if in fact the ground of the old cable is undersized for use as a neutral.
