Okay, let’s go back to the original quote that the OP is quoting.
It’s from St. Irenaeus’ book Against the Heresies (Adversus Haereseos), liber 3, chapter 22, section 4. Irenaeus has just spent the whole chapter, and indeed, a lot of the rest of the volume, talking about how and why God the Son, Jesus Christ, came and saved the world. In this chapter, he talks about why Jesus’ humanity would come into play, and this brings him to talking about why Jesus was born of a woman, and how that tied into Adam and Eve.
So then he says this:
“And even as [Eve]… having become disobedient, was made the cause of death, both to herself and to the entire human race; so also did Mary, having a man betrothed [to her], and being nevertheless a virgin, by yielding obedience, become the cause of salvation, both to herself and the whole human race.”
The Latin is pretty nice: “et sibi et universo generi humano causa facta est salutis”. However, “facta est” is not necessarily “become.” It could be “was made” or a ton of more passive-ish translations. God punished Eve and Adam and thus all humanity for the Fall; He rewarded Mary and Jesus, and thus all humanity. It could even be translated that Mary “brought forth” the Cause of all humankind’s salvation and her own, since “facta est” is occasionally used for that; but translating the phrase that way would cut off other poetic and theological meanings.
The other thing to remember is that “causa” in Latin doesn’t mean “the only cause” or “the ultimate cause.” It means “one of the factors behind what happened.” Eve was the cause of death. Adam was the cause of death. Satan was the cause of death. All three of these things are true. Similarly, Mary was the cause of salvation. Jesus was the cause of salvation. Abraham and Jacob and Moses and Joseph and David were the causes of salvation, too. They aren’t all on the same level of importance, but they are all causes.
So, back to St. Irenaeus’ nifty comment. It’s pretty clear that we are talking about things on a human level, not on the divine level that is actually the source of salvation. Eve disobeyed, Mary obeyed. On the other hand, we also have Irenaeus talking about how Adam disobeyed, Christ obeyed – and that’s a step up, because it’s both human and divine obedience.
It is certainly true that Mary’s “yes” was not her only act of obedience. Eve only had to face one big temptation, and then she fell. Mary faced temptations all her life, and never fell. (Same thing for Jesus, of course. But He was divine, and Mary was just a human.) It is also certainly true that any time the Jewish people obeyed the Lord, they contributed to God’s plan of salvation. So your analogy is not a bad one.
That said, nobody really touched the Ark of the Covenant to anoint it, except when it was first built and set up. Then it was anointed by Moses.