[JOHN COOKSON]

Wiring\switch.
Bypass the boat's wiring by running wire from the big cable connection on the back of the starter to the coil +. Or run a wire from the battery to coil + and see if the shutdowns go away.
Do not leave this wire connected and hot for more than a minute or two when the engine is not running or the coil will be fried.

Even though this problem sounds ignition related let's confirm by pulling the big wire out of the center of the distributor and holding it near the engine and check for spark while turning the engine the engine with the starter.* Do this immediately after a shutdown\no start before the problem cools off and starts working again.

* A remote start switch will facilitate this.

ex TRUE GRIT

Edit: Sometimes the insulation on the wire from coil - to the points gets worn away where the wire enters the distributor. Have a look see. These kind of problems will drive one nut-so. Been down this road.