As a new realtor (and student) you probably make below 80% median income which might help you qualify.I work with Finger Lakes Federal Credit Union (for my primary) and Lyons National Bank (for my investments), both will probably be able to help you navigating downpayment assistance and your situation. 

Often you can find these lenders with a mortgage broker or by reaching out to a local bank or credit union in the market you wish to buy.Cheers!

For VA loans, here are some solid options:Veterans United (veteransunited.com)Navy Federal Credit Union (navyfederal.org)Caliber Home Loans (caliberhomeloans.com)USAA (usaa.com)Not sure if I can post a link here in the forum. 

Get a line of credit from a bank that leverages your equity without refinancing the properties.3.

This one came from Massachusetts, a state where the eviction laws are not in the landlord's favor.

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

Freddie Mac will allow you to finance each property and the Maximum is 10 loans on credit.

This helps support a strong credit profile and a favorable credit score.One downside is the possible impact on your debt-to-income ratio should you seek to replace an auto, major appliance, etc. requiring a new loan just after applying a "chunk" to your mortgage.Deposit accounts, mattresses, extra monthly principal amounts, etc. each have their own unique advantages.

You could see if a local credit union or community bank will give you $20K.  

@Jeffrey Bourque Are you planning to finance this with a local bank or credit union?