As far as what we know so far is that she can shelter approximately half of her savings but would have to contribute the rest to paying for her care before she qualifies for Medicaid.

Presumably at some point, once you've built up enough equity through BRRR and made enough money through monthly cash flow, you would be able to get your initial capital out and yet keep "substantially all" of your assets in "qualified opportunity zone property" (90% for QOF and 70% for QOZB). 

I was pre-qualified for a mortgage last year but I unfortunately did not take any action on it.

Passive losses can only offset passive income (Unless your AGI is under 150k, phase out begins at 100k- or unless one of you qualify as a RE Professional- which if you both have full time jobs isn't very likely)So your potential passive losses from the Rental will carry forward until there is a time with passive income, and then it will reduce that.Also, much of those renovations to get that rental ready to rent will need to be capitalized.

This is from Housing Wire "Now, the Treasury has clarified that a business qualifies if 50% of its employee’s hours or wages are from inside the zone, or if the property and managers needed to produce 50% of the revenue are from inside the zone."

The problem maybe that with the payments on the 12 units that the lender may decide you do not qualify for the FHA loan, so it is probably best to close the fourplex first if you can. 

Do you have rehab skills? 

Though I have not checked with a lender yet I feel I’ll not qualify for a loan of about 750K given I already have 2 mortgages in my name of about 500K. 

And unless the topic came up in regard to monthly income that they needed to qualify for the home; there’s a good chance you are being manipulated.

In Dodd Frank, they anticipated that some might carry paper to get around Dodd Frank (not that you are doing this) and therefore they also "cast their net" over seller carry backs.Most importantly, please don't rely on what I say, except to inspire you to seek legal advice (which I am not qualified to give) from a qualified attorney in this area, and structure this so it doesn't get you into legal tangles or possibly worse, interaction with the CFPB.