Recent questions and answers about the "dubious" aspects of a Paleo lifestyle prodded me to investigate how women are viewed within it. There isn't much out there.
It would be enlightening to know what you consider to be the "dubious" aspects of living Paleo are. It sounds as if you are coming in with a bit of a vague bias, and looking for people to disprove it.
The question seems very similar in nature to the article http://paleohacks.com/questions/579/more-men-than-women-are-paleo, which discusses why there appears to be a larger focus on men in the Paleo lifestyle - primarily, because more men follow it faithfully. It might be worth a read, if you have the time and inclination.
Perhaps the way to begin to investigate it is to survey people who are participating in it.
Perhaps. But you will receive a larger sampling of males for the aforementioned reasons.
To begin, what do you think are important aspects to being a woman of child-bearing years in living a Paleo lifestyle? What about women who are of post-childbearing age? What do you think of defining women's roles via reproductive capacity? (It's pretty much done across disciplines, but that doesn't make it legitimate.)
First, Paleolithic living is not exactly "caveman / cavewoman" - it's a lifestyle choice primarily focused on maintaining your health, not on establishing or maintaining gender roles. Frankly, people have differing opinions on gender establishment, and that won't really change solely because of their living Paleo or not.
Important aspects to being a woman of child-bearing age in Paleo? Maintaining and sustaining your health, obviously, with a focus on being a sound vessel for a child to pass through (unless your desire is to not have children, in which case:)
Important aspects to being a woman of post-bearing age / do not wish to have children? Again, maintaining and sustaining your health. Being Paleo shouldn't change your priorities, merely make obtaining the goal of healthy living easier.
What aspects of Paleo-ism lifestyles are different than mainstream American/Western cultures? Other cultures?
Healthy living through intelligent and healthful choices, rather than ridiculous speed diets and instant exercise regimens. That still remains the primary focus of Paleo. If you are asking about gender roles in Paleo, then I still stand by my prior statement, that reestablishing gender roles is not a goal of Paleo.
What are some of the negatives for women living a Paleo-lifestyle? Why? How could they be minimized or eliminated?
Some people discover allergies and intolerancies much later in life than others, and any change in diet or activity can reveal these issues. For women specifically, I'd say that swapping your diet during pregnancy could lead to unwanted complications, and should be avoided or practiced responsibly. Some women also report that their periods change, and that they fluctuate in weight loss and gain during hormonal peaks after switching to Paleo. Being mature and patient are key requirements to minimizing the impact that these changes might have on your body.
What do women value as being important in a Paleo-lifestyle? What needs to be there to make those things happen?
Several women have already fielded this question in other comments / answers, so I'll just close with a reminder: Making a Paleo lifestyle work for you is your own responsibility. The things that need to be there to make your lifestyle work out for you are entirely internal. Patience, maturity, moderation, and commitment.