My opinion is similar to Wheatland KB. I would measure to see if you don't have some voltage at the start trigger terminal when the key switch is in the Run position. It might not be enough current to pull-in the solenoid, but it would be enough to hold it.
If this were a mechanical problem of binding in the solenoid, it would still be hung up after you throw the disconnect. When you put the disconnect back to normal, the starter would continue. By interrupting the ground, you force removal of electrical power. If I read your description right Richard, that takes the starter back to off until the key is turned to Start again. That means this cannot be a case of mechanical binding. Your problem is electrical in nature.:2cents: