The stumbling block is your saying only women. I might go to bat for gender equity, which appears to actually exist in Acts and has some implied Gospel sanction in the role of Mary Magdalene, the story of (another) Mary and her sister Martha; indeed the whole tone of the Gospels stresses general human equality.
I just can't see how one would go beyond accepting that a woman can be as good as a man for priesthood to excluding men from it. There's just no Gospel precedent for Jesus doing so, and nothing in the dynamic of late Rome that would give such a movement any traction.
To put it bluntly, why would men convert to such a religion? One strength of Christianity OTL was that it didn't exclude women the way Mithraism did. Children have a strong tendency to adopt and retain the religion of their mothers, Christianity could and did establish roles for women within the Church that strengthened it as an institution and I can easily see the parallel hierarchy of women within it growing to be more formidable than OTL. But not to the point of turning the tables and excluding men! Even boys raised to accept their sacral inferiority would be easily drawn, when older, to some countermovement that affirmed them, unless they had at least equality.
Why wasn't the reverse true, and why did Christianity not falter on the stumbling block of patriarchy? Actually, in my personal case, that's a big part of what did happen; I stopped believing, as I was raised to devoutly believe, that the Catholic Church and indeed Christianity in general, was the fount of Truth in large part because of the deep layering of the whole tradition with patriarchy, despite the very large counterweighting of that mindset with an ample legacy of women's powerful and inspirational roles; it seemed clear enough to me that at a deep ideological level the broad message of universal human equality and the specific examples of the importance of thousands of particular women was undermined by persistent patriarchy that had no place in a modern world and was always oppressive throughout history, no matter how rosy a light it was placed in. So I attribute the gender imbalance of Christianity as we know it both to the predominance of patriarchy throughout most of known history and the fact that Christianity grows out of such roots, and such gender balance as it has achieved is due to women showing their worth despite such ideology.
It is, in the last analysis, still a patriarchial religion. To adopt, develop, and defend gender equality, either through leveling roles and making them open to all, or through developing strong interwoven parallel institutions for women with a clear balance of power, seems possible (and good) to me. Maybe I'd still be a churchgoer and believer yet if that had happened. To turn the tables and actually limit men to a clearly secondary role--that's just not Christianity, it's some sort of alternative Goddess religion--at that, probably not a realistic one but some mirror-image caricature imagined and feared by patriarchalists with bad consciences.