Zechariah and Elizabeth

I've been studying Luke chapter 1. I'm sure somebody somewhere has done a thorough study of this, but this thought occurs to me: To what extent are Zechariah and Elizabeth deliberately represented as a picture of Old Testament Israel?

• They are old, but still barren. The Old Covenant has almost worn out - but still no Messiah.
• They were of the believing remnant who walked blamelessly before God, faithfully keeping the law - yet were still barren.
• In the temple, Zechariah prayed for salvation to come to Israel, representing that believing remnant whose prayer was heard.
• Elizabeth gives birth to a son who is filled with the Holy Spirit - old Testament Israel at last gives birth to the new age of the Spirit through the Messiah.
• Yet despite a clear word of promise, Zechariah fell into unbelief and asked for a sign. The divinely appointed time had come, but the people were not ready to believe.
• After a long period of silence, at last the promised son is born and Zechariah speaks again. (After 400 years with no prophetic word from God, the time of the Messiah suddenly arrives God at last speaks again).
• Elizabeth and Zechariah both echo the prayers and songs found in the Old Testament as they rejoice in God at last visiting them according to the promise.
• God's promised one grew up quietly, unnoticed in obscurity. God's purposes of grace amongst his Old Covenant people were often secret and hidden, whilst the nation at large went carelessly on its way, not knowing what God was actually doing amongst them.
  

Whilst this is largely speculative and I haven't thought about how an argument could be developed in a more rigorous way, I think there's enough there at least that the two of them are like Old Testament Israel in miniature.