This has happened a few times when we have purchased a property with tenants in place- one had 7 people living in a 2 bedroom apartment that needed a lot of work and the tenants weren't very happy about not being offered a lease renewal, and another that had a mean little dog who messed in the apartment and the occupant was not cooperative.  

If she cooperates through all of this and the buyers do their final walk through and she is still there (I'm sure she will have a great heartbreaking excuse), you are now getting sued for breach of contract because you stated the place would be vacant.

Naturally, we first try to schedule a time with the tenant, but if there is no cooperation or response, we serve notice and come and fix the issue.  

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I believe the current tenant will be cooperative since she has rented from me for 5 years without issues.

I would let her stay one more month but can I ask her a favor to cooperate with me to show the house to prospective new tenants?

If you attack them over their entire housekeeping skills, they'll be less likely to be cooperative, in my experience. 

It is legally (in most states) for damages only.I agree whole heartedly in the suggestion that you could wave all fees if the renter cooperates and a new tenant is available for the date they vacate.

That would probably make for happy neighbors especially if you will need them to cooperate later on.Then, after you have your plans for changing the use or whatever you goal might be, send another letter in the same manner to withdraw consent, your reason (you don't need a reason but it looks good) is that your use is changing, I'm planting strawberries all over my property, whatever. 

It helps them cooperate, they get something for their time, and I have no vacancy!