So you are thinking if they leave the lease agreement early then we will have no choice but to find a renter to replace them, instead of a buyer, as we would have if they stayed until the end of the lease agreement?

Not our first choice in neighborhoods, but the schools are top notch and it's a very safe and comfortable place to live.

As an alternative, you could always seek non-recourse financing for the Roth from a neutral third party.

If you have $20K down, additional money for closing costs and additional money for cash reserves, and the other factors (credit score and DTI) are OK, then you should be able to get a $80K loan.The other alternative is hard money. 

Having alternative collateral is one of them.

I wish I had better choices near me, especially when our tenants are driving us crazy.  

I plan to do one next year (refinanced out of my prior FHA on 4plex) for another 4plex that better suits my needs and neighborhood choice now.

Alternatively, if you have a good relationship or would like to build one, show up at the PHA in person with your question.

You made a great choice to jump in!

I have been exploring alternative ways to finance such as piggy back loans or seller financing.