Does anyone know how a flea market may be financed other than owner financing?

How much will be market and submarket and specific location dependent.  

But my state is a pretty quick evict state, our rents are somewhat below market, and we have extremely high demand.

That is a courthouse steps buy and not advisable in any way.If it is on the market, it is either a short sale or an REO.

As a new investor, starting in your local market where you have a better understanding is often advisable.All the methods you mentioned are excellent ways to begin your journey.

Perhaps focus on homes with longer days on market, ones that didn't sell during the initial two weeks because priced too high or needs updates but would still pass a loan appraisal. 

I can't tell what part of the country you are in but I bet there is one where you are...or one in the market you are targeting.  

It is a tough market and the easy money is gone.

Should I already have a property manager on stand by once I find a market that works for me?

If the software is not simplifying your life or making you more accurate, you shouldn't use it.Software does have extremely helpful features like online payments, marketing syndication (click a button and your property is advertised on multiple sites), electronic document review/signing, maintenance tracking, and owner reports.