Well, after brainstorming the problem for a little while, I finally decided to do what I normally do whenever I build puppets: I just ad-lib and pattern as I go, like a lot of people do when they fabricate, as seen in my YouTube videos.
I started with the little snoot-like protrusion that was giving me such a hang up in the first place; I cut the snoot to the shape I wanted it, but I also darted the inside of it to give it a little better front curvature, especially when viewed from the side.
So then, from there, I moved on to the back of the skull, and took a similar approach I take even I work on the front of the skull: I usually have a problem with my patterns whenever I build puppets, I can't usually retain a shape with the heads, and they always come out flat-looking, so I usually go ahead and glue a wedge of foam to the mouthplate, then pattern from there by folding the foam and figuring out the size and shape I want, then mark the foam where I would cut it, and glue it from there. That's pretty much what I did here, attaching a wedge of foam to the foam snoot, and figuring out where to cut; since I wasn't sure, I marked off two possibilities, and started with the larger cuts, that way if I need to, I could still cut down, otherwise I may have cut too much.
And this was the result:
And I took the same approach with the front of the skull.
Unfortunately, because I'm not a particularly good puppet builder, I ended up making mistakes, so I have to look for ways to remedy them:
Same approach with the jaw, and I tend to have problems with jaws when I have flexible mouthplates such as this, but I recently learned from a mistake I wasn't aware I was making: the edge of the foam that's going to be glued to the mouthplate needs to be slightly curved, so by doing that, I avoided having another puppet with a permanent double-sided sneer like Ella the Elf ended up with.
And the results; not quite cut right, but I don't believe that little open notch will be that big a deal... hopefully.
After trimming up any excess foa and dried glue, I was finally ready to fabricate; to help accentuate the shape of the snoot, I dabbled just a smidgen of glue onto the top of the foam snoot, and the bottom of the front of the skull.
Apparently the right lips didn't come in as they should have to match with the left; the lips were intended to thin out as the reach the front of the mouth.
Side view. I also added just a tiny piece of a foam wedge between the snoot and the skull, so the fabric wouldn't cause the face to look too smooshed.
And since I have to build two of theses, I copied the final results of this ad-libbed pattern so building the other one will be easier.