So you want to use your JD degree while in school, eh? Have you passed the bar? My wife is a lawyer in the health law [No, nothing to do with litigation, for those outsiders: she's been in court twice, once to be sworn in]. You may be able to find part-time work in the general counsel office of a hospital system? You might also look for local 501c3 places that may need legal advice with running non-profit clinics etc.
Often, the in-house people just manage outside law firms with issues (like HIPAA, M&A, malpractice, etc) and so they don't necessarily have to have a background in those areas of law. They might even welcome you if they know you have an interest in healthcare .
Certainly look towards your local university and see if they need help with articles of incorporation for med-student run health-clinics and the such. Doctors are always paying for contract review and negotiations. You may be able to pick up a small odd-job here and there...
Things that might not pay, but could bolster your application and that might be interesting to look into with a JD are special interest legal articles for various medical journals on ethics or current legal understandings of a wide range of medical topics. If you did any law-review work, you might find this very interesting. For example, even before graduating, my wife had a publication **in a national medical journal** regarding a review of current state and federal decisions on a very particular medical topic (not abortion, not euthenasia, but still very interesting to subscribers of that journal). Look around, and you can find a lot of physicians who like talking to JDs...
Good luck!