While I understand your statement, my ultimate question (as a good Protestant - sola scriptura, BABY!) was "Does Scripture make this connection?" I honestly don't recall Scripture doing this, but this could merely reflect my lack of knowledge about Scripture!
I'm pretty sure Scripture makes some mention of Jesus as the Lamb of God. Since He is the new Passover offering, the rest of the Passover analogy rides along.
SD
John's Apocalypse has an obscure reference to "Sodom and Egypt" with the attached adjective of "spiritual" which seems to tie Egypt to Sodom and a state of sin in one fell swoop.