A house owned for cash may under produce but it will almost never non-produce.But in order to completely avoid taxes on the boot in your 1031 why not purchase a second property as part of the 1031 using leverage. 

You have stable income that is a matter of public record and you are much easier to go after if you default.

These are small, non-warrantable studio condos, so no financing out there really.

Local government websites usually post them.

Anyone attending the government tax lien in Mayfield Ohio today?

You can get a loan on a non owner occupied property (1-4 units) that will have a fixed interest rate in the 4%-5% range right now.

Normally, online advertising has been all we needed to get the word out (to non-seniors) but I'm getting a lower than normal volume of calls. 

The additional time it would take to self manage a 4 unit portfolio over a 2 unit portfolio is non consequential.

Yash Bajpai go for properties that require a loan size and have someone to sign on the loan for you and you can get Fannie or Freddie non recourse lending at 5-6% for 30 years 8-12 loan terms.

In my non-expert opinion, I may be able to rent it out for as much as $800, but I certainly don't want to count on that to make the deal make sense.