Jasper, I do know that CFO has a desk at NAIA if that helps.
Your wife would need to organise a date and time with CFO so that they will ensure someone is there for her.
Food for thought

CFO Manila appointments are online now so I can't offer any current advice on securing the passport sticker at such short notice.

Your wife must talk with CFO directly to be sure.
Immigration will not allow her to board without the correct 'sticker'

Good luck and keep the forum informed