3 recent national studies show that the rent to value ratio is at an all time worse (what they really studied was cheaper to rent than buy, but there is strong correlation).  

This has definitely paid dividends for us when it comes to mortgage rates and lending options. 

Given your mortgage situation I would opt for taking out a HELOC.

Anticipation of these cuts initially moved mortgage rates downwards to their lowest in nearly 20 months.

New unit: 4-unit multi family in which 3 units (with existing tenants that will carry over from seller) will remain investment; I will move into (currently empty) 4th unit AND USE as primary residence with primary mortgage.

As mentioned have an attorney or title company draft the note and mortgage.

@Armando Carrera as others said above that’s mortgage fraud and not at all what an FHA loan is for.

I'm in Miami and want to invest in a cheaper market where my money will go a longer way and so I can cash flow better.

3 separate recent studies show it is currently cheaper to rent than own in virtually every large market and that it has never been more so than currently.  

Also mortgage rates are dropping.