But with the alternator connected it will blow the fusible link in substantially less than 2 minutes running?

Either the alternator is warming up in use and shorting, it's rare but possible, or your wiring is chafing/rubbing somewhere as it vibrates and shorting out.

Have you another, known good alternator to swap in? Closely inspect the heavy wire from the alternator output and make sure it has no bare spots.

As for the parts store test, I get skeptical about them myself.