I spoke to the prospective tenant's current landlord. 

I was told I needed a loan originator to qualify the prospective buyer for a loan even though my LLC owns the house free and clear.

Do not forget to do the math analysis and try to look at your prospective properties before you make an offer or at least use a contingency clause in the purchase contract that gives you some time (about 10 days) to make an upfront detailed inspection and possibly back out of the deal without a penalty that will hurt you too much.Follow up is crucial with potential customers as well as existing ones.  

I'll have the turnover regardless, so I'm not sure if there's a lot of benefit to holding firm.

I use Transunion Smartmove... have the prospective tenet fill out the online application.  

Team and prospective projects in place. 

Acquisitions team, renovation crews (fully licensed and insured), Property Management, and a Real Estate Investment Brokerage in case you ever decide to sell.By teaming up with a solid firm you can mitigate your risk and have some "boots on the ground" that have your best interest in mind. 

A law firm is selling it and the agent said the 135K is not bank approved.

You would have to go through a Mortgage Banking firm, but those loans are typically non recourse. 

I have hired a management company to screen prospective tenants for my apartments.