Credit Unions? 

Is this a credit union, local bank, national bank?

A lender (bank, credit union, second tier) is going to look at your income and your ability to service your existing debt (credit cards, vehicle, mortgage, rent, etc).  

Try a local credit union as they are generally more flexible with their requirements.

As far as your loan goes, contact your credit union, visit the bank where you keep your money, and ask friends and coworkers for their recommendations.  

BRRR) cash-out commercial/portfolio loans with Red Canoe Credit Union.  

Does anyone have any recommendations for banks or credit unions that will lend at least 500K with no closing cost, and the best rates?

Most banks and credit unions offer a traditional cash-out-refi or a line of credit (LOC).

I've been leaning towards my smaller local Credit Unions as opposed to the Big Names, because they usually don't send deals to another city or state for underwriting.

However, the VA Lender's Handbook (Pamphlet 26-7) cuts right to the chase and is the guiding regulation for lenders.4) NFCU Business Loans/Lines of Credit - Navy Federal Credit Union advertises business lines of credit, as well as loans for commercial and investment real estate5) Tuition Assistance / GI Bill - There are plenty of undergraduate and graduate degrees in real estate & property management; both in-house as well as online.