You are right the 1310 uses a Hitachi S114-381 starter. Different animal. DB has them for $145.00. I'd mess with rebuilding but I think New is the best option for me at this point since the solenoid is also bad. That would bring the rebuild (assuming $80.00 for a rebuild) to a little over $100.00. And I still have an old over spun.
If money were an object I'd rebuild. But for another 50 bucks, I've got a brand new one.