How did you "hot wire" the neutral safety switch? If you just connected together the 2 wires to it that should bypass that switch without causing your starter problem. But if you introduced an always-hot lead as "hot-wire" that would energize the solenoid & starter. Once it starts, disconnect the "hot -wire" and see if that helps.
Usually on the standard LH/CCW engines, replacement starters will be the lighter "noseless" permanent magnet type, but this one on the RH CW engine would be the old heavy type as I don't think they make the new type for that rotation starter. That difference shouldn't affect the wiring up, so as Stephen suggests, make sure the stbd is wired just like the port and no wires are touching others they are not supposed to.
Confirm the new solenoid terminals are labeled the same in same position.
You may have it wired perfectly, but it's always good to label wires and terminal connections and diagram them before disconnecting even when we think the connections are obvious before disconnecting.
http://slawecki.com/Penn Yan/Penn Y...uff/#single:crusader%20generic%20wiring72.jpg
http://slawecki.com/Penn%20Yan/Penn%20Yan%20Info/crusader%20wiring%20stuff/Crusader%20wiring%20diagram.gif?asatt=1&variant=raw
http://www.obbstartersandalternator...age-or-cause-the-engine-to-start-whats-wrong/
Don't replace anything w/o testing to find where the power is coming from. Does your ign sw. key easily return to the On/Run position or is it sticky at the Start position? Not a bad habit to wiggle the key a scosh when returning to ON from Start
Hope there is a simple solution .