Might not be the starter that's goosed but the solenoid instead.
I had the same problem with a Land Rover a few years ago.
I used to thump it with a big screwdriver if it failed to start.
One day I slipped with the screwdriver and accidentally shorted-out the contact from the solenoid to the starter motor.
This made the starter motor turn over properly and, after that, if it wouldn't start on the key I could leave the ignition on, short out the solenoid and get it to start perfectly every time.
IF you're happy to play with big lumps of electricity you might try something similar.
.
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if you can see the solenoid on a 2 engine.
Be warned though, you're playing with serious amounts of leccy and getting it wrong could melt the wiring, screw up the ECU or set the car on fire.
After 6 months of regularly starting my Landie with the screwdriver I gave up and got a new starter fitted and wished I'd done it straight away.
