1. I don't like the whole "woman's role" or "women in Judaism" terminology, for reasons that should become clear below. I'm just using it for convenience, because people know what it means.
2. The following is not a true paradox; like "woman's role", "paradox" is just a convenient term.
So here's my "paradox": The Rambam opened the door for the whole idea of a "woman's role", but I think he didn't believe that there was such a thing.
The Rambam is famous for promoting the idea of taamei hamitzvos, that we are meant to decipher a Divine Will behind the instructions Gd gave us. True, we won't comprehend everything, and failure to comprehend should not translate into failure to observe [see Hilchos Meilah 8:8], but we are meant to investigate mitzvos and discover Divine intent and philosophy behind them.
So it is that Kashrut may not be a set of disparate dietary laws, but a guide to healthy eating, or a unique diet setting us apart from the nations.
So it is that the laws of male haircuts may not be a set of grooming rules, but a way to distinguish ourselves from Egyptian priests.
And so it is that we look at a woman's exemption/exclusion from various duties, and deduce a greater philosophical picture of "How the Torah views women". It's an extension of the Rambam's approach to divining taamei hamitzvos.
The other hand:
The Talmud (Mishnah Kiddushin 1:7) declares that women are exempt from time-bound duties, unless we have an opposing lesson for a particular duty. Most authorities seem to view this as a prescriptive rule; when considering a woman's obligation in particular mitzvah, I can ask, "Is this time-bound?" And if the answer is Yes, then I can assume that women are exempt.
This rule leads to a taamei hamitzvos-style question: Why is the woman exempt from time-bound duties? Is it because the Torah's view of women is that they are dedicated to family and therefore they need their time free? Is it because they don't need the rigorous scheduling and structure that men need? And so we craft ideas of a "woman's role".
But the Rambam discounted the whole idea that this is a prescriptive rule. As he explained in his commentary to this mishnah, there are many exceptions to this "rule", and it is actually not a rule at all, but only a convenient-but-incomplete way to describe a set of duties from which women are exempt. The Rambam rejects the whole idea that we are meant to connect women and time in some philosophical way – undermining the "woman's role" that others have described.
This is probably wishful thinking, but I'd like to believe that when the Rambam dynamited the "time-bound duties" concept, he was really dynamiting the idea of a "woman's role" altogether. I find the concept of "woman's role" to be of the unhealthiest breed of taamei hamitzvos, placing a false face on the Torah's laws based on whatever fad is current, and so demanding that people come up with new roles that fit better with our zeitgeist, regardless of how well or poorly those new roles fit actual Torah, or actual women.
Sometimes a mitzvah is just a mitzvah, an exemption or exclusion is just an exemption or exclusion, and there are no roles involved.
[And speaking of role-busting, I made this three-cheese baked ziti with spinach for the kids the other night, and it was very good. I recommend the recipe.]