Per (b) 37 CFR 1.136:
"When a reply cannot be filed within the time period set for such reply and the provisions of paragraph (a) of this section are not available, the period for reply will be extended only for sufficient cause and for a reasonable time specified. Any request for an extension of time under this paragraph must be filed on or before the day on which such reply is due, but the mere filing of such a request will not effect any extension under this paragraph. In no situation can any extension carry the date on which reply is due beyond the maximum time period set by statute. Any request under this paragraph must be accompanied by the petition fee set forth in § 1.17(g)."
I cannot cite case law on this, but the language left so broadly defined is specifically designed to give more discretion to the USPTO. By such statutory construction in general, this should enable them that they will be prepared for unforeseeable circumstances so you should feel encouraged to reach out and plead your circumstances.
As it also reads: "[...]and for a reasonable time specified", but under no circumstances beyond the statute of limitations.
Per MPEP 2665:
My interpretation of (b) 37 CFR 1.136 seems on spot as the language you quoted from the MPEP clearly states so: "The requests will be favorably considered where there is a factual accounting of reasonably diligent behavior by all those responsible for preparing a response within the statutory time period" that is, if you can declare that you used all time reasonably available to you for preparing, and you still could not finish within the statutory time, that should be favorably considered.
I would also encourage you to reach out to your examiner off-record, on the phone, and just discuss it with them or ask your patent agent or attorney to do the same unless you feel it would otherwise be adverse to your prosecution tactics or strategy, they are typically co-operable.