Unfortunately, you have discovered the downside of having low rent. You are the best deal in town, so your guests don't want to leave! They will lie and manipulate to stay - I would.
This puts you in the uncomfortable position of telling them that they must leave.
It's not your fault that other places aren't as nice or as cheap as your place - nor should it be your concern.
Block out their last day.
Make up an exuse. "I'm so sorry, My Mother is coming from the hospital" "my son needs a place to stay" ...
Do not extend their stay and if they don't leave, ask airbnb for help.
Consider removing your 20% weekly discount