I'm an MD who works shifts, and we had a nanny with an unusual schedule. Although, I didn't have the overnight issue.
The keys to finding people, we found, were several.
We definitely guaranteed enough hours to provide an above average, full time salary. That way, our nanny wouldn't be pressured to find additional work. In our case, our nanny did some housekeeping/household management as well, as she was always paid for 40 hours, but normally ended up working about 30.
Second, although our schedule could vary, we kept our hours within certain time frames. So, we would only schedule her between 8am and 6pm on Monday through Friday, and one weekend per month. We also gave her her schedule 6 weeks in advance, as soon as I got my schedule. And, we told her to please give me any requests for days off, and I would submit them as my own.
We also, with her knowledge, scheduled the time so I could make it home on time about 90% of the time. That meant that most of the time, I got home early and she left early. Often an hour or two early. Once or twice a month, however, I would be unavoidably late. I was never more than an hour late, and we paid her an hour's worth of overtime.
For the right nanny, this was actually an attractive offer. A good salary, lots of weekday time off, and a fair amount of flexibility.
Personally, I love my schedule, and I could never imagine going back to a 9-5, 5 day a week job. You just have to find a nanny that feels the same way!
The nighttime coverage definitely adds another layer of complexity, but I wanted to tell you what worked for us.