I unfortunately cannot answer your query about credit life insurance.
It would seem if everyone is okay with the buyer being late in closing extending the escrow would be the simplest step
I do find it hard to believe that the final loan commitment is so close to the closing date. Not knowing your situation, know that in many cases (almost 50% ) escrows close late. When they do, the majority of the time (over 65%) is a problem with the lender...not throwing stones...just an FYI from CAR
(California Association of REALTORS)