Hi,
Sorry you're having problems.
I don't know this engine but I'm pretty familiar with the carbs the Keihin company makes for Honda outboards.
What you're describing sounds like you may have a stuck float inlet valve. The "freeze plug" is actually a cover for the right side bowl vent and that's where I might expect to see flooding overflow exit.
Not a lot you can do short of removing and cleaning the carb if you can't get that to stop happening.
If you can, try opening the carb bowl drain screw and shooting a bunch of carb spray in there.
Tap the bowl while you fill it and then allow it to drain. Do that several times.
Actually, do that for all four carbs.
If that works, then run a couple of tanks of Sea Foam or other fuel treatment/cleaner through her. Use the max dose mixture allowed.
Hopefully you can avoid a teardown because it's kind of a big job for anyone that's never done it.
But....it IS entirely do-able with a camera, a notebook, a shop manual and the carb manual.
And, doing it yourself will cost you WAY less than taking it to a shop where you're likely to get a $1,000 invoice and an outboard back that runs like crap because many of them don't know what they're doing.
Good luck.