Someone in the back needs to get down asap or they will probably die.
Right below you there is a suitable airport but the visibility is near zero airplanes are going around.
About 200 miles ahead of you there is another suitable airport with clear skies but the winds are blowing sideways at 34knots exceeding your company and airplane limitation.
What would you do?
Probably hit the airport 200 miles away.
My rationale:
1. IF you get in, when you land you're going to be waiting for someone to be able to attend to the passenger.
2. If you KNOW you're going to be able to land 200 miles away, you could make it in about 25 minutes if you're expeditious. Use that time to get as much information from the flight attendants about the passengers condition, forward that to dispatch so when you land, there's already a team in place, briefed, that can take care of the passenger.
3. If you're overhead at cruising altitude, it'll still take at least 10 to 30 minutes to do an emergency decent, set up for landing and chances are you'll go missed anyway, wasting far more than the 20 - 30 it'll take to get to an airport.
4. If it's +/- 10 minutes, the passenger is already probably dead if CPR/Defrib isn't working.
I might be wrong, but that's just how I see it.
No point in landing in Tulare, CA with a heart patient when you won't be able to get medical attention out there for another 20 to 30 minutes. An extra ten minutes and you can make Fresno with CFR on field and a hospital nearby that can dispatch a team.