I plan to sit on these types of properties for 5+ years minimum.Thanks.

I could just sit on my hands and wait 6 months for my properties to pull in enough cash to put a down payment on a house, but I want to go go go.So my question is as follows:    How do I "Afford" to get my next mortgage?

Unfortunately the owner of the property has dementia and could not recall we had ever met or spoken.

Talk to some other tax pros, file an extension, and don't leave a bunch of money sitting on the table for no reason. 

I plan on sitting down with him next week.

After all expenses: mortgage, cap x, vacancy, management fees, I will cash flow about $200.00.There is a lot of mixed messages floating around the internet so I’m torn between walking away and sitting on my capital, or just moving forward and going with the flow.

Our landlord eviction bill is sitting on the governor's desk. 

As I said, you can get a HELOC not as a private client, but pay a little more, and as I recall, somewhere around 1/2% to 3/4% back in 2014.Normally, the first 10 years in the life of the HELOC is interest only, and interest plus principal beyond that up to 20 years or so, and you'll have to pay off the principal at expiration.

They're all sitting home anyway collecting paychecks from our tax dollars

Good chance you'll have a property that is sitting vacant, with no one allowed to work on it, and you'll be paying hard money costs.