OK: I'll assume you have a four cylinder Mercrusier...135 Hp at the prop. (depends on the year) Earlier years were HP rated at the flywheel. Later years were rated at the prop. I'm not sure..but I think the transission came around 1993. You seem to be pretty savy with motors.
Faulty ignition coils can overheat and short out internally....Then recover when they cool off. They are usually bolted in direct contact (steel to steel) with the engine block OR intake manifold, as in the V8s. This contact contributes to the coil overheating.
Replace the coil.

NB
EDIT: Running fine at the dock is NOT the same as running fine under load..underway.