Above you mentioned that coverage on the dwellings wasn't that important so if you wanted to keep cost down you could use the more basic DF1 policy (ask the agent down there) and market value for the dwelling coverage amount with a higher deductible and then max liability limits (probably $1 million). 

Your mostly conventional approach is limiting you. 

I agree with @Chris Sellers that your next step is to begin narrowing down your market choices.My best advice:Be ruthless with the numbers - Be crystal clear on your financial objectives and how you'll measure success.

So what do I do - especially with limited cash for now??

@NhiQuann Jones from my limited knowledge, if you have a property that is paid for in all cash, say $50k... and you put in $30k of renovations... and that property appraises for $100k... you own a $100k property outright.  

I want to avoid personal guarantees and limit my cash outlay as MUCH as possible.

It really depends on how much equity you have in your primary residence.You could also use the HELOC for down payment and cash reserves for any rehab or maintenance needed.Then once the property is stable you can cash out refinance to pay your HELOC back and replenish reserves.With the limited information provided this would be my suggestion.

However, I live in an expensive market (NYC) and so will likely have to be limited to buying an investment property out  of state so that it can cash flow.

@Neil Haven a four unit property will qualify for many commercial programs, which may be the way to go.With a commercial policy, you may have more flexibility with choosing the building limit and can pick and choose which coverage's you want.I would suggest calling a local Independent agent. 

We are just wondering, again since this the 2nd time that someone limited the time to 3 hours, if it was just the inspector we want to use and our own expectations that are in the way.