That is backward; speak to a PM before you pull the trigger on investment property, not after.  

I have pulled lists, had skipped traced, made calls and have seen very few promising leads.

They may not want a larger down payment but may be interested in your cash reserves or where you would pull money from (HELOC, partner, another business, etc.) if you had a decent repair to tackle.Don't forget there are other creative financing options that do not include a bank.

Considering that they should be out and are basically pulling a fast one on you (POA's should be negotiated during the initial contract signing, not after closing), I would charge the very upper end of market rent and demand a large security deposit.

Airbnb says they pull external ical feeds every 5 mins (good but not great). 

My question is whether I should pull the $180K increase in equity out of the first property (which I can do using a HELOC on the investment property) to finance the downpayment of a second property, and if I do, how to treat that in my analysis. 

My plan would be to complete a $150-$200k remodel, but I wasn't sure if by pulling permits it might jeopardize the grandfathered status of the property.

We paid cash, but are currently looking to put a mortgage on the property in order to pull out the cash that we originally put in the property.

He talks about buying a house a house though has yet to pull the trigger because of the "neighborhood".

If that is the case, it doesn't matter how much it costs you to carry your property - that is what it will rent for.You can ask a real estate agent to pull rental comps for you or just look on Zillow, FB, CL, etc. for your own comps.