I'll respond to your question through my lens, colored by years in telecom...I learned a lot about how things work!
Why not consider multiple mentors, including from outside your organization, for your high-potential women? I realize that your goal is to develop "from within," but if the resources aren't there then encourage your 4 women to look outside as well.
You could utilize the expertise of the women professionals inside your organization for various learning opportunities other than those a sponsor could provide. You could also teach your protégées how to recruit additional mentors/sponsors based on their learning/career goals. One of the best mentoring programs I've ever worked with is sponsored by a professional association and the protégées learn very valuable professional and political insights from mentors in other organizations.
While it may not be within your current definition of "mentor," your 4 women could develop relationships with "sponsors" who may be most interested in promoting talent. Not all women leaders are interested in doing this, and the same applies to male leaders. Might you identify senior leaders who are interested in keeping great talent and encourage them to work with these women, not as "mentors" so much as "talent scouts" who could--in several professional conversations--learn and encourage their strengths? The relationship would be more of an organizational "look out" rather than an individual mentor. It's also possible that the relationships with senior male leaders could develop into mentoring with both parties defining which aspects of the "work hard, play hard" culture are a fit.
I encourage you to broaden your definition of 'mentor' and look at your program through the lens of learning, recognizing that mentors can be many and for short or long periods of time. Even in a highly political organization, younger leaders with diverse values are changing the cultures to be more inclusive.