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. 

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

You mentioned you didn't want to use equity as purchasing power though so maybe it's not a good method for you, nothing wrong with that.

@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.

They have no ability to foreclose or evict.And it should say they fully understand the risks of this transaction and agree to accept those risks.You probably want help from an attorney or someone who's done a transaction like this for that disclosure.You also want a power of attorney from them for the property so you can deal with anything that might involve them in the future.

@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.