The current situation is abominable; due to poverty, cultural barriers, and bans on spending federal money for abortion it's already effectively impossible for reservation women to obtain. But. If the surrounding territory bans abortion, there will be a large demand for it, and some of those people will have plenty of money.
Numerous tribes have already weathered the tempest to build other facilities such as casinos. They could do the same with women's clinics and bring in tons of money -- a course that might appeal to some tribes who voted down a casino. This would also make a big improvement for native women, whose risk of sexual violence is now more than 1 in 2 rather than the 1 in 4 of other races.
At least one previous attempt to build a women's clinic on Pine Ridge failed due to some tribe members opposing it. But while the effort was active, fundraising went quite briskly. That means any tribe that can muster the political support can probably gather financial support.
So as a multicultural approach to problem-solving I propose:
* Remember native women and two-spirits when building networks and fundraising for abortion access and sex education. A way out for them is a way in for others, and those connections will benefit everyone.
* Seek out reservation health providers that are NOT federal, and donate to support them. It sucks to be dependent on people who wish you were dead, and that's how it is with the federal health care for tribes. In particular, look for scholarship funds that support educating native doctors, nurses, paramedics, etc. If we can get a clinic movement going -- which reservations already need, remember -- then it would help to add new scholarships specifically for reproductive specialties, an area poorly served by the mainstream health system. Students are more likely to choose those if they see solid financial support through school and jobs afterwards.
* Investigate historic records about women's status in various tribes, their access to family planning and other health care; and compare with current conditions. Some tribes have been or are much more woman-positive than modern American culture, and these tribes may be more receptive to leveraging current politics to bolster access to reproductive care. In many ways the modern situation is dire, but in some tribes women are pushing back and gaining ground.
* When people argue that a casino is a poor choice of income for their tribe -- you'll see the green frog skin argument a lot, and some tribes have banned casinos -- then propose a health clinic with reproductive care as a different source of revenue. This would benefit everyone's health. (If they don't like that either, try green energy or green building, which are also congruent with most tribal ideals.)
* Watch for clinic proposals in tribal news. If you see one, encourage it and support it however you can.
* Spread the word about these ideas through tribal, activist, and other channels. The more people who hear about them, the greater the chance someone will pursue these opportunities.