Dear Hope,
As-salamu alaykum
Thank you for your comments and soliciting my opinion on the word / phrase in question. However, before I part with my humble opinion, I would respectfully like to draw your attention to my last post where I attempted to disconnect Prophet Abraham's trial with the need to sacrifice on the Hajj pilgrimage (22:36-37).
There is no explicit connection. One does not slaughter an animal because Prophet Abraham did during his personal trial. These impressions are sought from Islamic secondary sources and not the Quran.
From a Quran's perspective, the sacrifice is part of the Hajj ritual and not in memory of Prophet Abraham's trial. This is often a misconception.
As far as the term 'bidhib'hin azim' (37:107) is concerned, the word ‘azim’ simply means 'great' or 'mighty’ and the word ‘dhibh’ simply means 'a sacrifice' or 'something which is slaughtered'. The verb from the same root 'dhabaha' also means to slaughter or to sacrifice no different to what the Children of Israel were asked to do as recorded in Surah Baqarah (i.e. to sacrifice a heifer – 2:67; 2:71).
Hence: a great / mighty sacrifice.
It is important to remember however, that a contingent of the audience of the Quran were also those of the previous scriptures who would have been familiar with the story and the sacrifice of the ram from their own Scriptures (Genesis 22).
However, just to reiterate that from a Quran's perspective, whatever prophet Abraham sacrificed as part of his trial with God has nothing to do with the sacrifice that is demanded of pilgrims during Hajj, at least from a purely Quranic perspective.
I hope that clarifies, God willing.
Joseph