I agree that I don’t WANT to move my family there but In 5+ years that could be an entirely different story.... and that’s kind of what I’m betting on.

I think it’s better to rent, but if you’re fixed on buying, I think getting roommates in a townhouse would be the best bet.

That's a rough story with your GC I bet that's a common story.

If you are wanting to BRRR, then you can use your heloc to purchase and rehab a property or a combination of that and hard money to find a duplex.I work with a bank that will Cash out refinance once a tenant is placed and will lend based off of the asset and income production, not based of my debt to income ratio.

Asking for suggestions on what cities are best...but here’s my real question, is it better/safer to use a HELOC or do a cash out refinance for downplayment for another property? 

Assuming it is a purchase mortgage, your lender is correct.The disconnect is probably from reading about refinances and/or old pre-recession info and/or reading that you can roll some of the closing costs into a higher interest rate (but not loan amount).

Or would I have to refinance my current home and pay off the first FHA loan?

You’re betting on appreciation and choosing to lose money monthly (rather than increasing a down payment) to make that educated guess and keep capital in the bank.

For example, can I pull out a HELOC on them, refinance them, and use the funds from the HELOCS as a down payment for property #3?

Here are a possible option: Use the BRRRR strategy, buy value add Multi-Family, Rehab them, Refinance out, and Repeat.