Intermittent problems are for driving boaters nuts! However, since you've bypassed the Neutral Safety Switch, and if you did it properly (jumped across the circuit), you have a working knowledge of the design of the engine along with its circuitry.
If it were me.... the first thing I would do would be to start cleaning all the cable and wiring terminal ends of the starter circuit including the battery terminals themselves along with the ground at the powerhead... also clean the components they attach to, then tighten them securely with a wrench or pliers... not your fingers if wing nuts are encountered. This would assure that there are no loose, or tight but dirty connections that would result in a voltage drop.
Of course the ignition switch could also have an intermittent problem but that's most unlikely. If the problem is encountered again... using a small jumper wire... jumping from the "B" (battery) terminal of the switch to the "S" (starter) terminal to bypass the switch. If this cranks the engine over BUT the key turned to the START position does not... replace the switch.
