Been there and done that......while in nursing school, and continuing on as a new grad, I had to work on holidays. Never had that issue before, and discussed with Rabbi at length. Bottom line was it was a greater mitzvah (obligation, not "good deed" for the uninitiated or misinformed!) to care for the sick and dying than it was to observe any holiday, shabbat included. It was a greater evil to turn away from the injured, ill, or terminal because of "holy" requirements....and that worked fine for me.
When I had the opportunity to shift my schedule (paid my dues?) I arranged to work Saturday nights into Sunday, Sunday nights, etc....and when I went to days, I worked every Sunday through Thursday instead of Friday or Saturday. I often switched holidays when it worked best for myself and someone else.
Irony is that I have a non-Jewish husband and have had to do some seriously creative scheduling to accommodate his family's holiday visits/desires along with my own! Yes, it CAN be done