John, I will answer from my understanding -
We believe "fulfilment theology" not "replacement theology."
"Literally" needs qualifying - the prophecies are fulfilled by Jesus & the Gospel as real, living, born again from above, come into the whole New Covenant family of God by repentance & faith in Jesus. Believers form a "holy nation" that transcends earthly divisions. That "holy nation" is called "the church."
A distinction between the Jewish/Israeltite believers in Christ, & the unbelievers is necessary to avoid confusion. The use of "church" effectively begins in Acts 2, where it is comprised entirely of Jews & proselytes.
The Biblical term "church" includes a local gathering of Christians (as in all the letters to churches) & also includes believers in general when referring to what you refer to as "the universal church." (e.g. 1 Cor. 10:32, 12:28, throughout Ephesians, Col. 1:18, 24, Heb. 12:23)
Many thousands of Israelites welcomed the Gospel, beginning with John, and continuing through the Gospels, including Jesus' entry into Jerusalem. From Pentecost onwards the true, believing Israelites turned in repentance to Jesus. To avoid confusion, these believers were called in Scripture "the church." They were, however the true Israel, the believing people of God, "my people" (e.g. Zec. 2) called out from the sinful nation that rejected their Messiah. In Romans 11:1-6 God owns these believers as a faithful remnant.
It is clear from Peter's Pentecost sermon & his sermon in Acts 3 that The OC promises & prophecies to Israel were being fulfilled by Christ in his FINISHED work, and in the Gospel of salvation preached in Jesus' name.
Acts 3:22 For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you. 23 And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people.
24 Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days. 25 Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed. 26 Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.
Thus it is clear that the promises to Israel are indeed fulfilled to the believing Israelites who formed the church. The Gospel was never closed to the scattered Israelites, & Paul made it his priority to preach to them in every synagogue he visited.
BUT, because the Jewish leaders rejected the Gospel, the term "Church" became used for Christians in general, as well as local congregations. Paul could hardly write his letters to the Israelites or Jews, who continued in unbelief.