@John Teachout We both agreed that a month-to-month addendum would be a good solution.

First step is realize your need for a home for your family doesn't negate what land lords/PMs require to rent to you.Second step and a possible solution is to the problem is put yourself in the LL/PMs shoes so you can understand why they have that requirement. 

To say this differently, the minute you suspect they've given up or are stringing you along, then yes....lower the boom and issue Pay or Quit.Here's one solution to getting paid: put them on weekly rent payments until they recover the full amount of their payment. 

This is fine and it is a viable solution but you have to choose the management company via extreme vetting.

@Thomas Meyer  I would like to do a more cost effective solution like that next time I have a vacancy, but these people were so determined I'm not sure if that would be adequate.

I fully agree with @Nancy Bachety and I like the concierge solution suggested by@Anand S.

You are going to need skin in the game unless you can find creative solutions like owner financing, friends/relatives happy to take a second lien position or whatever. 

I hope you're able to find a solution.

If her concerns are reasonable, then she's a valuable asset to the team, thinking critically and pointing out potential issues you may not have thought about so you'll have solutions ready if they arise. 

It is not a deal killer, but certainly presents risk when the entire park could be out of a sewage solution if the septic has a problem.