I'm not going to tell you that you're utterly wrong.
Rather, I'm going to tell you a little bit of history.
I don't believe that the Catholic Church started really keying up the "Immaculate Conception" issue for many years after the time of Christ. But that doesn't mean that the doctrine was made up out of wholecloth to fill a hole in Catholic theology.
Rather, there existed (and exists) a very ancient, proto-canonical text, one used by the early church and which was included in some early lists of the canon (not in others). It didn't make the canon; neither did the Didache of the Apostles, but both are orthodox documents. Both are acceptable to read and consider in the Church.
This very ancient text is the Proto-Gospel of James. It purports to be written by James, brother of Jesus, and recounts quite intricate details of the inner workings of the Holy Family. It contains the account of the virgin birth, the flight into Egypt, Mary's life, Joseph's age, the reason Joseph took Mary as his wife, the reason why one would not expect that marriage to be consummated, and - most importantly for these purposes - the story of how Joachim, father of Mary, and Anna, Mother of Mary, came to conceive Mary, the angelic visitations and circumstances surrounding this.
I want to emphasize that this was a very ancient document, not something devised by the Church once the theology of the Church became more sophisticated and the conundrum of Original Sin and Mary arose. Catholics didn't make up the doctrine of the Immaculate Conception out of wholecloth. Rather, they got the idea from a very ancient First or Second Century text, which might have even come from James, writing from WITHIN the Holy Family about things that he knew from his particular vantage point.
Now, it is true that the proto-evangile is not in the Bible, but that is not important from a Catholic or Orthodox perspective, because the Catholic/Orthodox Church never did view the Bible the way Protestants do, so the fact that a Tradition is in or out of the Bible doesn't vitiate (or strengthen) it's authority in Catholic/Orthodox eyes.
The Orthodox, apparently, do not read the Proto-Gospel in a way to see the remarkable conception of Mary as being an answer to the problem of Original Sin, the way Catholics do, but they certainly read the document and observe that Mary was, from conception, a special girl with a special destiny, ordained from the beginning.
So, this is the thing about your post that I think is mistake. You think the Catholic Church "made two miracles" to explain one. You presumably think that the Immaculate Conception was conceived in the heads of men. But actually, someone alleging to be James, from within the Holy Family, wrote down the story of Mary and Joseph, and the very remarkable circumstances surrounding Mary's conception, long before any medieval churchmen started puzzling through the issues of immaculate conception and original sin. There was always this persuasive and orthodox document out there, from the very earliest time, describing the angelic involvement in Mary's conception. Immaculate Conception, avoidance of Original Sin, specically chosen from before birth to be Theotokis - all of this fits in with that text. It gives a rational explanation as to why God did that, not the other way around.
It is not true that the Church just made up the concept of immaculate conception out of wholecloth in order to solve a medieval theological riddle. There was always this text about Mary's supernatural conception. That text inspired an answer to the problem of Original Sin, and the supernatural events described in the proto-Gospel may have been given the name "Immaculate Conception", thus giving them a rational basis, a reason for being. But the Church didn't make it all up. At worst, the church formulated a doctrine to explain why God went out of his way to cause Mary's parents to have such supernatural occurrences at the time of HER conception. She was foredestined, by God, to carry Jesus, from the moment of her conception.
To suggest then that this conception was Immaculate is not much of a stretch. It gives it meaning and makes sense. Whether the conception was really immaculate or not, there was a miracle, documented from the First or early Second Century on, about a miracle that occured at the time of her conception. The Church didn't fabricate a miracle. There WAS a miracle in the ancient texts. At worst, the Church ascribed an explanation to the miracle which gave it a function in solving a theological problem.
As I noted above, the theological problem of the Immaculate Conception gives Mary a womb untainted by Original Sin, but creates a new problem: if Mary didn't have original sin, she shouldn't bear the curse of Adam, and should therefore have been immortal. From this comes the great question as to whether Mary DIED or merely fell asleep and was carried bodily into heaven. There are bones and bodies and artifacts of a great many saints. We probably have Jesus' burial cloth, at Turin. But there are no relics of Jesus: he ascended into Heaven. And there are no relics of Mary either, which is interesting. The doctrine of Mary's assumption into heaven and the real lack of a body leave open the question asto whether Mary bore the price of original sin at all. Maybe she didn't die, because she was immaculately conceieved. Maybe she fell asleep and was taken into heaven.
We don't have any accounts of an AGED Mary, and this is important too. Assuming Mary was 15 at the time of Jesus' birth, she was almost 50 when she stood at the foot of the cross. St. Luke gives such detailed treatment of the life of the Holy Family, such personal details, that it is always assumed that he had direct contact with Mary, spoke with her, etc. But that would have been at least 15-20 years after the Crucifixion, so by that point Mary would have been in her 70s. If Luke's Gospel was written AFTER the destruction of Jerusalem, Mary would have been 84 years old, at least, when she talked to Luke. Was she OLD?
We don't know.
It didn't make the canon; neither did the Didache of the Apostles, but both are orthodox documents.
While you make the very valid point that the proto-gospel of James is a very early document, constructed prior to the official pronouncement of the perpetual virginity of Mary, you are perhaps overstating the case for the book in your argument. The book is orthodox for Catholics. Its scope is rather limited, however, focusing almost exclusively on Mary's life. It has two troubling features for me. One, it purports to have been written by James. This was almost universally discounted by the early church, which was the primary reason for its exclusion from the Canon. Secondly, it has such a singular focus (establishing the purity of Mary) and attendant fantastic details (not fantastic in the sense of necessarily untrue, but fantastic in the sense of fantasy) that it fits well with other apocryphal works.
Rather, there existed (and exists) a very ancient, proto-canonical text, one used by the early church and which was included in some early lists of the canon (not in others).
This is a bit overstated as well. To say it was listed in some early lists of the canon is not really significant when one considers that not Irenaeus, nor Tertullian, nor the Muratorian fragment, nor the Peshito, nor Tatian's Diatessaron, nor the testimony of Justin's writings consider proto-James as a part of the Canon.
I want to emphasize that this was a very ancient document, not something devised by the Church once the theology of the Church became more sophisticated and the conundrum of Original Sin and Mary arose.
You make a very good point here. But, the proto-gospel of James was written in response to the questions of the virgin birth of Jesus. That is obvious. It is almost the exclusive point of the work. So, while it was not constructed to solve the problem of Original Sin vs. Incarnation, it was to solve the problem of a virginal conception and the assertion of the early church that Mary was sinless. This (in my mind) "need" of the early church to claim that Mary was sinless hints at an already developing tension in the theology between sin and the incarnation, with the need to explain the impossibility of a flawed human carrying the divine. You will, of course, see it differently.