What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

I'm not sure what your local options might look like with a small community bank or a credit union. 

Look carefully at the credit card transfer checks.

If you want to do some flips or BRRRRs then you could consider taking out a Line of Credit against the three properties so you can use the cash with interest only payments for a short term project and then pay it back and then use it again (Lines of Credit are revolving - meaning you get to keep using the money).

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

This is basically an unsecured personal loan, like a credit card.

Working with local credit union to refinance at lower than market rates

I do not use the lease agreements provided, I use the promulgated contract provided by my state, but it's perfect for background/credit checks, docusign, and payments. 

Portfolio loans, asset-based lenders, and home equity lines of credit are all alternatives to traditional borrowing.

You can get up to 75% of the ARV on a cash-out, with rates starting at 5.875% APR and a 680 minimum credit score.