Thanks for your astute observation. The wife will concur that I think I know everything...
It sounds like vapor lock to me. The fuel system cannot pump fuel vapor and can only pump liquid fuel. Even though the fuel is pressurized, raising the fuel boiling point, once the fuel gets hot enough it changes state from a liquid to a vapor, cannot be pumped and the engine cannot operate properly.
There is LOTS of thermal mass to the engine(s), two in my case, one in yours. While operating, cooling water is removing that heat into to the raw water, w/ about a dozen means using that water flow to remove heat from the various engine systems, while the engine is running.
Once the engine stops, that cooling flow also stops. All that thermal mass is sitting inside a well-insulated "sealed" box, the engine compartment. The box is insulated and sealed to contain audible noise, but it also contains heat.
My boat had ZERO vapor lock problems in New England.
My boat always had vapor lock problems in southern Florida.
The boat would always vapor lock when stopping for an hour with the engine compartment closed, with the symptoms you've described.
In my case, the only way to prevent vapor lock was to open the engine compartment when stopped, but that doesn't work well w/ guests lounging in that area.
There are two initial steps. First, ensure the exhaust has not deteriorated. It should be possible to continuously hand hold the entire exhaust while the engine is operating after it reaches normal temperature, except for the port immediately adjacent to the head where the exhaust gas exits.
Second, run through the checklist in the Mercruiser 99-7 Service Bulletin. In my case that was followed to no effect.
In my case, operation of the existing blower system had zero effect on the problem. The intake for the existing blower system is down low, as-required to properly suck out possible heavier-than-air fuel vapor collecting in the engine compartment.
It may be that those blowers would have sufficient heat removal on your boat while parked to keep the temperature low enough to prevent vapor lock. This is my suggestion as an attempted solution to the problem. Run the existing blowers prior to shutting down and after getting underway to see if they provide sufficient heat removal.
Another potential solution is to keep the engine compartment open when stopped, so the hot air may naturally exhaust via air convection. The open engine compartment lid doesn't work well with people lounging on the boat.
https://images0.boattrader.com/resize/1/21/8/6812108_0_091020181714_21.jpg?t=1301731
https://images0.boattrader.com/resize/1/21/8/6812108_0_200820181317_45.jpg?t=1301731
The solution I implemented years ago was instead to design, fabricate and install a custom thermostatically-controlled high-air-flow heat exhaust system that maintains the engine room temperature to the setpoint by automatically toggling these new blowers on and off.
This new heat exhaust has provided 100% problem resolution on my boat over the years since I installed this system.