Definitely look into the 3-11 evening shift. My wife has been working this shift since she became an RN about 3 years ago. She's not an elite runner by any stretch, but she's found the time to train for a couple of marathons in which she qualified for Boston. She would get home from work between 11:30 and 12:00 (usually), sleep until 7:30 - 8:00, then get up and do her training for the day. Another benefit of evening shift (versus days) is you have off time while it's daylight.
That said, evening shifts can often be harder to find. Her most desired work places just starting would have required her to do some kind of alternating 12-hour day and night shifts (switching every six weeks or something). She wanted no part of nights, so worked in a less desirable hospital (generic community hospital, medical floor, mostly elderly patients) on evenings for about 8 months before switching to her current job (Children's Hospital, surgical floor) which she was able to get the evening shift because she did have just a little bit of experience.
Nursing is a hard job though, she is constantly on her feet and busy--I routinely get calls during her short dinner break at 9:30-10:00 pm. Apparently, this is particularly true for evening shift (at least if the hospital also runs 12 hour shifts).
One final note: when you start going for your NP, it will be REALLY difficult to find the time. One of my wife's best friends just went through this, and time was certainly a premium. Depending on your ultimate priorities, I would consider holding off until you have met your running goals.