Hi Brad,
Yes, pretty strange Indeed.
I have to say up front I have never worked on a Honda 90 nor have I ever experienced this problem.
The limp mode and buzzer description makes me think oil pressure or cooling. Those are the only two things that should be a reason for that.
You didn't mention any lamps.
Taking a BIG leap of assumption, I'm guessing it's probably not a low oil pressure situation because you say it's been running great for years even with this "annoyance" happening.
Looking at the parts pages, I see this outboard is equipped with two flush valves and two cooling system pressure relief valves.
I'm wondering if something is happening inside the cooling system, disturbing flow enough to affect the temperature sensor
when you trim the outboard in?
It would have to be just enough of a temperature spike to cause the sensor to trip the engine protection system to cause the power derate. That's a question, not an assertion because I certainly don't know.
I could be waay off but that's where I would begin looking.
First at the thermostat and those pressure relief valves and springs and then possibly pull the water jacket and see if there's something going on inside there.
The salt water outboards are known for large buildup happening behind the jacket cover and it's possible a chunk has been floating around in there. Again, JUST GUESSING because I've never actually seen that happen.
It looks like the temp sensor is a one wire type so you could try temporarily taking the wire off to see if that changes anything. Item 19 in link below:
Just advise you not to run the engine long without it or damage could occur.
I also see that the oil pressure switch is at the top of the engine block and might be easily accessible. Item 11 in link below. You might want to take a look at that since an issue there could cause the limp mode you describe.
Wish I had some better troubleshooting advice for you but those are the ideas I came up with for this.
Good luck.