Well, if I understand your post, you took out the old stat and the alarm didn't sound. But, when you replaced it with a new one, the alarm issue returned, correct? If that's the case, then that salt "crud" has probably really "choked" down the pathways that the water takes during warm up and hot water is being trapped up in the head (where the overtemp switch is) after the thermostat opens and is setting off the alarm. When you shut the engine down briefly, the water pressure from the pump subsides and allows that trapped, overheated water to drain away and cooler water is allowed to take it's place after the pump starts working again because the thermostat is still warm and open. Then the alarm stays off.
Stated a bit more simply, the passages need to be flushed. Not so easy on an outboard because of the open nature of the cooling system. I don't deal with salt issues so I haven't had to develop an effective flush procedure. But there should be a few guys here on the forum that should have some good suggestions as to how they go about it.
As far as your power complaint goes, I would think that outboard should be MORE than adequate to do the job on that RIB. I'm assuming that you don't have a tachometer since you didn't mention RPMs. If the motor isn't propped correctly for the load, she may just not be reaching the best RPMs for doing the work. I would suspect that you would need to see around 5500 + to push that baby with a full load. If it's not getting there, then it is more than likely a prop pitch/diameter thing. Sometimes experimentation with different props is the only way to achieve the goal but getting props to "play" with can be difficult and/or expensive. Sometimes shops will have some "loaners" on hand for you to try hoping you will buy a prop from them if you find one you like. It never hurts to ask. You should list your prop pitch and diameter here so that the guys on the forum can do some "cipherin" and try to help you come up with a solution.