Regardless of the state, no non-compete prohibiting you from working in an entire industrial or business segment within 50 miles is enforceable to the best of my knowledge. Non-competes are enforceable when limited and when specific business knowledge is involved.
Obviously there is no knowledge attributable to that one company that would be transferred to a competitor. Clearly the hospital is not a competitor. Clearly the 6 person company is not an industry leader or even of any consequence, nor would have trade secrets of any value.
Obviously a 6 person company does not have the resources needed to try to enforce such a contract in court and I would give their chance of winning such a contract claim at slim to none.

