That's interesting. Maybe if you have in-house counsel and can have someone on salary easily go after a doctor it's financially worth it?
The OP's scenario seems like something well worth paying a lawyer for an hour or two of time to review the contract exit options and proceed accordingly.
I assume that a without cause termination option is included in the contract and giving the required 60-90-120 days would shield you from liability, and assuming you have 4 months before starting, you could give that notice and not have to report for work. That being said, I assume many employers would not necessarily even require the notice, even if you technically would have to report for some amount of time before the end of the without cause termination period. Who would want a doctor to show up to start work to satisfy a 17 day obligation?