Also would consider getting a POA from the seller for their loan so you can communicate make payments on it.

Instead of denying them, can we refer them directly over to the owner for them to sign a lease with the owner who is willing to effectively manage the contract, payment and relationship BUT would still want to retain us (albeit for a lower fee) to deliver ONLY guest and property care activities (guest communications, organizing cleaning, lawn and pool care etc). 

You need to have criteria designed to protect your money, and a reliable method of determining value.In my opinion, appraisals are not necessarily a reliable method of determining value, so staying within your own market area to start with can also protect your capital because it's easier to know value next door than across the country.

Look into house hacking, BRRR method.

What's your preferred method for Background/Credit checks and Applications?

Make sure you have all your communication.

Hi Christina,I am the CFO for a Pinellas Property Management in TB FL and I use the following methods when verifying income for military personnel. 

If you have a method that works for you that's great too.

Brewer method is famous   you can google it 

Get authorization to use them to reestablish communication if she is ever incapacitated, incarcerated, or deceased.