Will the refinancing of the appreciated value of your rental cause your debt service costs to increase and put you in the red?

Lot of red tape but about as cheap as money can get in this scenario. 

That is a red flag.

Due to the size and zoning, it seems a win/win.The house has lots of issues and is just 1600 square feet, and the potential for income is of course better by improving the site.I'm hoping to tap into knowledge on this site.  

I budget $1,000 per year for maintenance and $.67 per square foot for capital reserve on average for a single family. 

I wouldn't toss the deal away but work it so that I could still get it (assuming the numbers are good) and at the same time, protect me from any downside risks (like dealing with an eviction).From the story you received about their reasoning, red flag, red flag, red flag!!!

From looking at your numbers....margins aren't strong here and you could easily go from black to red working so tight.

The 1900+ square foot 3/2 is fully furnished, has WIFI, new appliances, new smart TV.  

Ryan D. to answer you question on a previous thread I am on the North Side, Portage Park, Albany Park and Lincoln Square) .  

The A/C guy just put more freon in it, he basically patched it up for another year.....Also with a heat pump the techs DO NOT put extra freon in your unit when they installed it to compensate for the 50-100 foot lineset/pipes that run up the wall, so you are already short on freon the day they install the unit, you just dont know about it....If you went with a package unit (the square rectangle kind that is all outside) you shouldnt have to worry about being short freon because  its precharged from the manufactor (I trust them more than a green helper that just started in the A/C business), and you shouldnt have to worry about carpenters, or sheet rock guys punching a nail threw the pipes that run up the side of the wall because its all self contained in that outdoor unit...Thus they call it a "Package Unit."