Hi Katrina~
I think you are really onto something; and I very much appreciate how you've sought to incorporate a variety of biblical values and perspectives - that is to say, you recognize the importance of the divine covenant, the need for human response, the singular call to Abraham, the expansion of the mission to the Gentiles. Those are all very important pieces of the puzzle and I think it's really cool that you have recognized them and crafted a response that includes them all (essential to good theology!!!). Way to go!
My answer is quite similar to yours (and offered as AN answer, not as passing on THE answer...no one has clearly defined "the answer").
I first agree with you that covenant is essential to the answer. The whole of the biblical story is predicated on the belief that YHWH is a covenant-keeping God. The idea of an eternal, unbreakable covenant ratified by a single-party begins the story of salvation (see Gen. 17). And likewise Paul will draw upon that same idea to explain what Jesus has accomplished (Gal. 3; Eph. 3, etc.). God made a promise to Abraham to be the saving-God to him and to his descendants.
But the promise given is not merely to be savior to Israel, but - as you know - THROUGH Israel to be savior to creation itself. Thus Abraham/Israel is an essential element in the story of restoration, but not the exclusive beneficiary.
The question, remains, however: Why ISRAEL? They proved a very mediocre (at best!) collaborator in the program of redemption. And surely an all-knowing God would be aware of this in advance. Why elect such a rebellious partner?
And here, the me who has been listening to WAY too many lectures on game theory - would ask: What were the alternative strategies? Suppose God decides Abraham is a bad choice? Who would do better? Babylonians? Canaanites? Californians? And the short answer, of course, is: none of the above.
My guess is that Israel does...what humanity would do - rebel rather frequently against the Lord. It wasn't Israel that rebelled in the Garden, it was just plain old humans. God then chose a sub-set of humans to help set humanity back to rights and the sub-set, turned out to be...human.
Which is actually very important, then, for understanding what was accomplished on the cross. If it turns out that Jesus is the fulfillment of Israel - what Israel was always intended to be - and Israel is simply a sub-set of humanity, then Jesus is what all humanity was intended to be. (The NT understands Jesus as the chosen ONE; Israel came to her perfection in Jesus - he is what Israel was always called to be but could not be. Thus if Jesus IS Israel, and Israel IS humanity, then Jesus is humanity as humanity was intended to be.)
And - for reasons we have discussed elsewhere - it is Jesus as the culmination of humanity that is essential to the work of salvation.
Thus your question being such an important one! To really understand the cross, we have to understand humanity's relationship to God (which we see displayed by looking at Israel as a microcosm of humanity). And what we discover is that - for any part of humanity to be saved - God will have to do the saving. It is not that God needed to choose the right humans for the project to be successful (and thus we can't understand such a bad choice as Israel). The real choice is whether God is going to choose to redeem humanity or not (as choosing Israel is a bad choice, but there exists no better choice).
When God chose Abraham, God chose us all - he chose the cross. It was a free decision to pay the cost of redeeming a people who would very clearly not be redeeming themselves (indeed they'd generally fight their own rescue). But God chose anyway (and - looking at Abraham, Moses, David...Peter - we might say he chose the runt of the litter so as to only further prove his point: God saves because God is a loving God, not because the objects of his love are so inherently lovely).
That's a first draft, so hopefully clear enough. But let me know if I only muddied the waters.
Thanks for the good question and and the insightful search for a response!
K