I know they say you get what you pay for but I am impressed with this STR PM, and I use Steesa and Innago. 

The hang up is getting deals formally drawn up.One idea:- I buy the property and pay 25% DP, then they provide capital after the closing and I pay them P&I over 5-10 years.

Use that loan to pay the back taxes and get things under control.

For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

There are quite a number of things that can make utilizing an FHA loan more difficult such as more barriers during appraisal, appearance of low qualification/little cash, typically longer closing period, likely higher interest rate, and PMI cannot be dropped without a refinance if 3.5% down.That said, just chain 5% down conventional loans, and make sure your duplexes pay for themselves.  

I would focus on the house hack and not take a pay cut.

buy house  find renter rent house maintain house pray they pay rent and dont destroy it.

You can't directly do something to allow you to sell the flip, and buy the triplex without paying gains. 

After fully renovating both units, I refinanced to pay off the loan and held it as a long-term rental.

They didn't pay for it, so they don't take care of it like an owner.Before you make assumptions about costs based on a seller's contribution to improvements, find out what they improved?