I am not sure what the air-path is that you are describing here:
"the inner gap between the housing and the blue ring."
If you look inside the main tube with the blue ring on, you will see a gap between the ring and the Sylphyo's body. The upper part of the Sylphyo is not airtight and it doesn't have to be, because the mouthpiece seals the main tube when pushed in, making the instrument playable. Only in your case does this seem to be a problem because the small channel to the electronics is not completely closed. Even with the mouthpiece in place, moisture can get in over time, but with the mouthpiece off, moisture will definitely get in there. As Laurent said, the hole to the electronics compartment needs to be sealed.
Since I have no experience with Hot Glue, I have many concerns with attempting to seal the active mouthpiece port.
Will I melt the plastic of the body of the Sylphyo?
No. The melting point of hot glue is lower than that of the Sylphyo.
Will I drip glue into the active mouthpiece port and into the Zone of Electronics?
No. Hot glue is too thick for the small hole. It won't go in easily.
Will some undreamt-of calamity befall my Syphyo in my fledgling attempts at Hot Glue Art and I'll be left playing a kazoo at gigs.
No. And as we know, Kazoos have moisture problems :-)
Let it warm up and try a few times somewhere else, then you can go for the Sylphyo. If it doesn't work right away, just let it cool down and pull away with your fingers. If you put the blue ring on immediately afterwards, it's fixed just like Aodyo did.
That was an awkward description. I meant that you immediately put the blue ring on the hot glue to fix it. Only if the glue application is unsuccessful, you allow the glue to cool briefly and remove it. The glue is softer than the Sylphyo and it doesn't attack the plastic. It's a mechanical bond, not a chemical bond.
I'm sorry if I sound incomprehensible at times. My English is not good enough for technical precision and Google Translate is smart, but from what I can see it cannot be trusted for technical subjects.
I believe that the O-Ring on my black mouthpiece does not make a perfect seal, since there is a very slight wobble in my mouthpiece when it is fully seated. Not a problem playing, but maybe there is a slight moist air leak back up underneath the blue ring.
Maybe yes. But "slight wobble"? I would say my mouthpiece fits quite well, at least as well as you can expect from a piece of plastic with an O-ring. The conical shape is well done. My spare mouthpiece fits the same way. However, I think two O-rings would be better for the fit.
But your O-ring isn't dry, is it? It shouldn't be. There are silicone-based care products for O-rings and seals in general. I have one of the type used for scuba gear, but there are many. Search for "silicone-based lubrication for O-rings".