I think overload is out as a cause:
He said he had a functioning circuit breaker.
Overload would have tripped that breaker.
If it does not trip, there is no overload.
If the installation is only marginally following any electrical code, or reason, everything in the circuit will carry at least
the amps the circuit breaker will permit.
That is what a circuit breaker is designed for:
Breaking the circuit BEFORE anything starts smoking.
Catalina might have been a bit sloppy, but putting in circuit breakers that allow enough load to start cable fires would be criminally insane, and they sure are not, and did not do that.
That pretty much only leaves a ground fault (less likely, because the sizzle happened to happen under load), or a high resistance, almost open contact.
Either way, whatever happened, happened in the outlet box. Repair/replace.
PS: A short circuit is pretty much the only thing that can't have happened: That would have triggered the breaker, without time for sizzling.
No, you should not simply buy new units, plug them in, and be on your way.
You have no idea what caused the failure, and could cause a fire and lose your boat next time.
Either you overloaded the circuit, or you suffered a short circuit.
If you have suffered a ground fault, and had GFCI outlets installed as the surveyor recommended, the outlet would have tripped, saving you from damage.
It's impossible to know for sure what went wrong based on the limited information you've provided. Find an electrician and get it fixed right. Not only will you save your own boat from burning, but perhaps your neighbors' boats as well.
I just noticed that you were running the space heater and the iron. Most likely (but not definitely), you have overloaded the outlet and melted down the guts of the outlet, or perhaps the wire in the run somewhere.
I suspect this was a 15 amp circuit, and the iron and space heater took you up to 14.9 amps. Not enough to trip the breaker for an overload, but enough to "boil the frog", and melt down the wiring.
For future reference, do not continuously load a 15 amp circuit more than 80% of it's rating.
15 * .8= 12 amps. Don't continuously draw more than 12 amps on any single 15 amp circuit. That's for the whole string of outlets on that 15 amp breaker, not 15 amps per outlet.