Quote: "The closest airport having landing minimums is 1:30 away."

I would want to make sure that the above mentioned airport would have landing minimums at ETA. I would call company and get them involved in selecting a suitable alternate, something may be further away but may have better weather and inform them of the medical condition along with ATC to insure priority handling. I want to avoid the situation of getting to the closest airport only to have it go below minimums or having to do a missed approach. I would multitask and have the FA ask the guy/gal if they ever had this happen to them before and if they carry nitro pills with them and get ready the defib equipment if carried on board and of course 100% O2 for the person.