I haven't done a bid, but I have made two qualified applicants bid to see who'd pay the highest rent. 

I have my thoughts, but I do not feel qualified to comment.

If it wont cashflow I would look to 1031 exchange the property if possible into something that will you would want to get a qualified intermediary for that so its done correctly but you may be able to end up with cashflow and appreciation in another property!

The reality is you can rent more house than you can qualify on a mortgage.  

I spent a lot on improvements on a rental this year (hvac system, new flooring) that usually I would have captured on my tax return but I’m worried that the lower AGI is going to affect how much I qualify for for the new house.

You can also try to qualify for SNAP through Family Services.

I have started my own form of syndication (not formal, just investing with family), and wanted to remove a blight from the neighborhood while at the same time building momentum for my new business partners.

Is the bank giving back the difference to the owner or the owner needs to submit a formal claim?

One challenge you might run into is that a lot of lenders will want to see two years of rental receipts to count that towards your income so you want to make sure you will qualify for both loans.  

I'm still learning here, is this something that I qualify to look into, and is this a good idea?