Nice description of how the lock plate works. Your analogy to the picture frame hanger is spot on!
The SE valve receives voltage (12v) as soon as the engine starts. The valve is very similar to an engine thermostat as it has a wax pellet inside that expands when heated. The voltage going to the SE valve powers a heater coil to melt the wax. That takes time..2 to 3 minutes.
Your description of the engine sputtering and starting to falter after only a few seconds indicates that the SE valve is probably not the reason. Although, I would be testing the voltage anyway.
You asked much earlier in this thread about a vertical brass tube that you could see when looking past the throttle plate. That would be the low speed emulsion or "jet set" tube. See item 18 in the link below.
If you didn't remove and inspect/clean that tube and hose out the passages in the carb body that tube feeds, that could be the reason the outboard won't run.
There's just SO MUCH to cleaning these little puke carbs, it's almost impossible for a novice to get it right the first or....even.....the tenth time!
They defeat long time carb rebuild guys (like me) and are the reason I have TWO copies of the Honda Marine Carburetion Manual on my bookshelf! Because, I wasn't successful my first few times either.
Hondadude, a much respected, missed and LOVED contributor on this site told me to buy that book. He had one too!
Sorry you're having so much trouble but, at least now, you know that they require special care and feeding if you want reliability.
They're actually amazing devices at fuel delivery and economy but not after getting plugged.
I used to try to explain every cleaning detail but eventually it became evident that most want a "quick fix" and ignore more than half of what I write. I get it, IT'S A PAIN.
I have NEVER failed to "recover" one of these carbs but I stopped trying to get all others to and no longer argue if a guy just wants to bolt up a new one. It's way faster and often cheaper for some in the long run.