CMG,
I have a standard OMC cobra, so I don't know if this will be the same for your setup, but I had the same issue in years past.
In my case it was the ESA Interrupter switch was just barely triggering after I had made a slight shift cable (trunnion) adjustment.
My shifting was smoother, but that slight adjustment made the Load Lever pull just enough to trigger the switch.
AND
It only happened at the lake when there was a load on the outdrive/prop. Only during the holeshot and then resolved itself if I could get moving. And it didn't happen every time. (right on the edge of triggering)
It would NEVER happen when I had the boat on the trailer and running on the muffs.
I even had this happen after installed a "power prop".
My best guess is that the extra load on the "power prop" and the slight miss alignment of the trunnion and knurled knob made the load lever rock a bit more than normal. It then in turn was just enough to trigger the switch to interrupt the motor.
I resolve my issue by reading up on section 15 of the SELOC OMC Stern Drives repair manual and making the proper trunnion / knurled knob adjustment.
Make very small adjustments to the trunnion as large adjustments can bite you with very hard shifting or jumping in/out of gear.
My boat is a 1992 5.0L V8 and has the interrupter switch.
My dad's boat is a 1986 V6 and also has an interrupt switch.
However, our switching linkage is very different even though both are OMC cobra units.
Hope that helps.