If someone on the property wanted to sue your business, the LLC would limit the liability you have to the assets that are in the LLC.

As fro 1031 exchange deferment there will be limitation. 

If your insurance in predicated on a non-smoking building, yet you have smokers in there that you know about and don't do anything about there may be an issue if there's a loss from a cigarette caused fire.

I hold my investment properties within an LLC, which on paper, after all deductions, should take a loss each year (or close to it). 

@JT Crownover  the reason for my list was an exercise in where one can buy houses under 10k in the US and those are the easiest for someone who has limited backing or capital can actually wholesaleit does come down to the greater fool theory though.. and I am certainly aware of West Jackson I had my Plane Hangered at Hawkins field and would drive through W Jac to get to it ... :)  felt odd driving through a neighborhood that I could buy a house for the same price it would cost me to fill my tanks with Avgas ..

What is the best way to accomplish this while limiting the expenses associated with accessing the equity? 

Rent roll, profit and loss statements and expense report are not trustworthy.

In calculations of gain / loss on sale you should use allowed or allowable depreciation. 

Something else to consider with units over 4 bedrooms is that Minneapolis has a limit of 4 unrelated people per dwelling.

If you are going FHA I would assume you limited like most entering that cash down is the issue.