Before you purchase a property, I would suggest going to your bank and applying for an increase in your credit card and line of credit limits (don't use them, just have more space available).

It seems to me that there's a hard limit on how far they can rise without tanking the entire economy given the level of public and private debt as well as the impact on financial markets. 

The limitations on those loans is not that you can have up to 10 conventional loans. 

I'd give it a try since your time is limited with getting a tenant in before vacation.

Parking in NYC is limited.

You will have an entitlement limit of let's say $450k, you could in theory buy two homes in different areas if your total loans between 2 homes are under that $450k.

That seems steep, I pay $550 for the same type of SFR with Allstate but you may have different limits than I

Most bid jobs have a time limit which is usually 30 days.

The “dead equity” argument is that the ROI on your equity when you have a paid off property is very limited.  

Looking for some advice, because the wife and I are at a loss right now!