I think we have to look at what we know and then possible significances.
I know they made coverings of leaves while God provided clothing of animal skins.
From a practical point of view, given that God cursed the earth and Adam would have to work the ground, the change makes sence.
Symbolically I do see this as illustrating God's provision (similar to God making the clothes of the Israelites not wear out during the exodus from Egypt, and Jesus' words about not worrying about what to wear because God would provide).
I am not against this and yes, these other passages you are citing definitely speak of God's provision as we are faithful in whatever God has called us to but seems a bit of a stretch to apply it here in Gen 3. The main theme here is the fall and redemption and we cannot get away from this nor should we. The skins certainly was a gesture of God's grace and I don't know if you were a "Covenant Theologian" back when you were a "Calvy" but I would say that the "Covenant of works" and "Covenant of Grace" seems to fit quite well here. Dispensationalists typically refer to this as the "Age of Innocence" and the "Age of Conscience" but both are looking at this from a redemptionist standpoint.
I have not thought much about it, but you are right that it showed Adam and Eve the significanceof death. This would have been their first encounter. It would also give them knowledge needed to survive outside of the Garden.
I am certain it would be an object lesson they would not soon forget!
And I can see how they would understand this death was to provide for them.
The cursed world was dramatically different from the one Adam and Eve knew in the garden. God would still provide and there is still grace but they have to live with the consequences of sin for the remainder of their lives.
We have to kill in order to survive and provide sustenance and every time you have had to kill in order to provide meat, clothing, shelter, or whatever, you would be reminded of this! Jerome posted some of Calvin's commentary regarding how the coats of skin were a reminder to Adam and Eve regarding the ugliness and severity of their sin and that these skins likely were not the most pleasent of things to wear and perhaps they even carried the stench of death. The scriptures do not say whether or how well God "Tanned and Preserved" the skins prior to making clothing for them! But yes, we are drifting into speculation here and need to be careful of this. I believe that Jerome was trying to refute something I had said but I thought that Calvin's comments actually gave some good insight that I hadn't considered before.
Of course another thing to note is that mankind was either vegan or vegetarian prior to the flood. God told Noah that he could eat meat in Gen 9: 3 and this is the first mention of a carnivorous diet meaning I am not sure how much was going on in the way of "animal sacrifices" prior to the flood.
Likewise the Israelites sacrificed animals as "gifts" of obedience but this also provided the blood the priest would use to make atonement for their sins.
I have heard you make mention of this a few times now. Would you say that the blood is what makes atonement or is it what the blood represents? I would go with the latter and here is why.
Leviticus 17:11 tells us that
"The life of the flesh is in the blood" and we understand today from a scientific standpoint that it is the blood that brings oxygen and nutrients to our flesh. Without blood, we cannot live!
Exodus 12:13 says
"And the blood shall be to you for a token upon the houses where ye are: and when I see the blood, I will pass over you..."
The underlying Hebrew word is
lə·’ō·wṯ (226) which according to Brown-Driver-Briggs means a sign, pledge, or token and when I think of a token, I often think of the old game rooms in malls back in the 70s/80s where the machines took tokens rather than quarters and you had to feed your dollars into a change machine in order to get these tokens. Of course a token tells the machine that you have paid the price but the token was a representative but not the actual currency that you had paid. In the same manner, the blood was token of the fact that a death had occurred, that a lamb had been slain in place the firstborn (substitutionary atonement once again, just cannot get away from it!) and the blood placed on the door and side posts was indication that a death had already taken place and the Angel of the Lord would pass on by. Hopefully this makes sense. I know nothing about Hebrew and am completely dependent on the tools here! Perhaps we have a Hebrew scholar who can chime in here and provide additional insight?
My ultimate point there is that the blood is a sign that a death has taken place. It would not be enough to just let some blood out of a lamb, bandage it up, and put its blood on the door. The lamb had to die.
And with the crucifixion the death of Christ was a necessity for us to be cleansed. I would even say it was necessary that the Jews be complicit in Jesus' murder (in a way the sacrifice system was a warning about what they were doing).
Everything from Gen 3:15 on pointed to Christ and his finished work of redemption! I was thinking about the reason why after his resurrection, retained the wound in his side and the nail prints in his hand. When we look upon them, we see grace, mercy, and the reason why we are able to stand before him as being joint-heirs with him! I don't think we will ever get over such a sight! What does a lost man see when he looks upon Jsesus's scars at the Great White Throne judgment? How about the Parable of the Vineyard in Mt 21:33-41 where the wicked husbandmen slew the son of the vineyard owner thinking they could take it for themselves? I believe they will look at those prints and see nothing but judgment, that they are just as guilty as if they themselves had driven the nails in Jesus's hands!
So yes, I can see God killing an animal to illustrate what man would do in the future. But I think saying it is a significance of the event rather than an illustration we might apply may be pushing it.
I am trying as best I can not to read into the passage more than what I should. As I have said, I am leaning mostly upon the progressive revelation we see as we dig further through the books of Moses.
Got another hour and a half in the air.
Isn't it cool how you can be online arguing theology at 35,000 feet in the air? We certainly live in intersting times!