As @Dave Metsker suggests, you can time the release of funds to keep your PR seller and estate heir/beneficiaries in a cooperative mood (and avoid adversarial threats from disgruntled family).

You don't say how much but this type of credit problem is often easy to resolve with a little effort and friendly cooperation.

If I make it easy for them to leave, they will usually cooperate.

It seems that a tenant would realize that there is a real estate transaction happening and would probably go to that bad place of "There's nothing good for me in cooperating here".

If you're willing to pay the selling agent a commission, state "Will cooperate with broker on sale" or" will pay x% commission to the selling office".

On top of everything that has already been discussed, a conventional lender WILL NOT PAY an assignment fee and generally do not cooperate on double closings.Their title department is going to ask why the contract is with Person B and the current name on title is Person A. 

@Chance Cooper Typically once you qualify for the loan/close on the loan and have lived in the required amount of time.

If they don't cooperate, get a locksmith to change the lock (or change it yourself if you can access it from the inside) and provide copies to the tenants, preferably before you change the lock.  

Remember, all necessary facilities are available to the property: Gas, Alabama Power (not a cooperative), Cable, City water etc.

Time frames will be about the same, depending on the quality of the loan officer/cooperation of the buyer.