If it's ずらり it might be "lined up / in a row" as in one person behind the other or one-by-one. The phrase could be interpreted as:
I can't go, one-by-one I can't go
That is, in other words, slow motion
クビにする means "to fire someone" as you said. It is rarely used as other meanings.
The sentence before you refer to is 朝一のアラームほど許せない輩はいないでしょ. 輩 is used for a person, not for objects. ヤツ is the same as 輩. So this lyricist regards alarm clocks as humans. That is "personification".
Daijirin (三省堂 スーパー大辞林) lists the meaning of 首にする as:
(1) 解雇する (to fire someone)
(2) 首を切る (to behead someone)
Maybe that second one fits better in the song. Then again, maybe it just means that they dislike the alarm clocks so much that they would just fire whoever made them.
Judging from the whole lyrics, I must say this part is intentionally constructed so that it looks somewhat like "word salad". Throughout the lyrics, there are quite a few randomly-appearing words whose grammatical roles are not clear to me (e.g., 鼓動, 眩暈, 思春期, ...). Maybe you have to stop trying to parse them as a grammatical sentence. (Unfortunately many ...