I love what you're going for, and I think the palette is just about perfect.
The head is nice, but the mouth is forming into sort of a smile, almost laughter, whereas almost every pro team logo with a face on it is usually scowling or trying to intimidate in some other way. I actually kind of like it (in part due to its subversiveness) but I don't think the team would want to go in that direction. You mentioned the eyes need a little work, too, and on that note I'd just add that they appear to be looking up at a master rather than howling at a moon. That submissiveness along with the mirth cast by the mouth make it feel a little too unserious.
The other concern I have about this one is if that softer red you're using as a background in both of these images is the team's primary color (and I think it would have to be, if either of these logos were to be used), the head doesn't feature nearly enough of it. Obviously you want it to contrast with the rest of the jersey, but aside from the eye, the head has none of that color at all.
I find the moon and cactus visually appealing, but I get a very Looney Tunes vibe from the way the cactus is skewed, and again I think that cartooniness sort of undermines what most teams try to go for in their jersey. Generally, hockey teams want to look tough, or at least impart something that would intimidate an opponent (if not toughness, then speed or skill or even history and decorum).
Speaking more generally, while I appreciate the presence of the moon and the cactus in addition to the Coyote itself, I think both would benefit from a more southwestern aesthetic. I don't think you need to go full kachina like the original logo, but more of a nod to the unique elements of Arizona and its culture would make it feel more sincere.
You're definitely on a good track, though, and I'd take either of these over the current logo in a heartbeat (and as an art student, you're hardened to much tougher criticisms than the ones I have to offer, I'm sure). Keep the mockups coming.