OK my wife, Filipino PP holder (in Maiden name but amended in manuscript to married name) went to Manila (from Spain but same rules same as flying from UK) with a month left on her PP.
There was no problem with the 6 months validity rule, as she was going to her home country. Had she been stopping off in say HK that might have been a problem. (i think the six month rule would have been applied).
A couple months before she was due to fly, we made an application to renew her PP, in her married name, and made an appointment with DFA in Manila. The DFA help line is 24/7, We called on a Sunday and got advice.
She subsequently got the new passport in Manila (lot pf problems with paperwork errors in DFA and it was issued with a variation on the surname which had been amended in the old PP)
I called the airline and gave them her new ID (passport name and Number) no charges. She flew back no problems. The flight was booked in a name which was slightly different from that in the new passport,
(Just for reference. In Spain Spaniards have two surnames. When we had wife's PP amended in Phil embassy on Madrid, it showed her first name, and then my surname and her surname as a double surname,. The passport subsequently issued in Manila showed first name, my surname as her middle name and her surname)