WRA. Using the rebuilt starter sounds like a good choice. Nevertheless, I'd be tempted to tinker with gear on the old starter. Maybe liberally spray the shaft and gear with penetrating oil. Leave them set overnight. Then tap the gear a few times in the morning with a small brass hammer while liberally squirting more penetrating oil. Keep repeating the process until the gear break loose and easily slides up and down the shaft. Then I'd be tempted to try it out and see if it starts the engine. As you can probably tell, I'm easily tempted. 8^)
Jack E/NJ