Do you have one of these? OMC Electronic Shift Assist "ESA"
The OMC Shift Dogs have an angled face of either 2deg or 5deg. This makes the dog difficult or impossible to disengage when there is load on it. The ESA is designed to drop the idle for less than a second while the engine shifts. It does this by interrupting the ignition to a couple cylinders during the shift. This takes the load off the drive momentarily so the clutch dog can disengage.
If the ESA is not adjusted properly, it can interrupt the ignition when it is not supposed to, or not at all. My experience with a 1987 OMC Cobra, with the 2deg dog, was that you really did not need the ESA to shift, it just made it easier, but because of stiff shift cables and worn parts, it was too difficult to keep it adjusted, so I bypassed it by bending the arm on that long switch in the middle of the picture away from the lever. However, if you have a 5deg dog, the ESA is much more necessary.
BTW, if you were to turn off your ignition for a split second while shifting to nuetral, and turn it back on before the engine died, you would be doing about the same thing as the ESA, so you could try that as a diagnostic tool (but not a permanent solution).
Look up "OMC ESA" or "OMC Electronic Shift Assist" to find information on diagnosing and adjusting the ESA system