Hello @Jennifer--And-My-Brother0,
When a guest's checkout time passes you and they are no longer covered by any help, support or insurance from Airbnb.
The stay is over at that time and guests must be out unless some other arrangement is made.
This guest hasn't responded to the offer of booking another room and has made off the record, by phone, offers to pay you, which she can always deny.
Why are you worrying yourself about her and asking other guests to change their arrangements?
It sounds like she has the whole house in a state just because she won't bother to pay the booking rate for one extra night.
She's the one who should be asking nicely and going the extra mile to make sure she books the extra night.
Sounds like she knew you hadn't enough free nights for her in the room when she booked but she decided to just try it anyway.
I'd get her out the moment her original check in time arrives. I've no idea if NYC does any checks on hosts but if they do and she's out then you've no worries.
Steve.