If it is almost done, maybe you let them all walk and start fresh.

If they’re moving to the area fresh, well, odds are your month to month lease might be a intended segway for then, especially if they have a history of owning rather than renting. 

The reason why we don’t kick the tenant out is: most likely I will lose 1mo of rent and we’ll have to invest some money in order to make it ready for the next tenant like fresh paint and other little things.

@Jay HinrichsI just listed (10 mins ago) a freshly cleaned up rental in Pen Argyl (slate belt) on FB marketplace for a client.

Everything is clean and fresh and fixed up when the new tenants see it.

Our cleaner lives down the road so she can go by and swap tanks if a renter runs low, but when a tank hits 1/2 full, I pull it and put on a fresh tank then go get it filled.

This was a freshly rehabbed property where the neither the leak nor resulting mold growth was obvious in a visible inspection. 

The rehab will include framing-in part of the basement to create a 4th bedroom, and then doing fresh carpet, paint, appliances and counter tops throughout the house.My contractor didn't feel like a building permit would be needed until we decided to frame in that bedroom and he realized that there would be some electrical work needed (both in the bedroom and to clean up some DIY wiring by the current home owner.)    

Let the Seller deal with his problematic tenants so that my client gets a fresh start.

What about looking to hire a real estate consulting professional to help navigate and provide some fresh eyes, that can independently look at this situation from afar, hear the objectives, run the numbers and help you all come to a solution?