I do the math on every single opportunity that comes up to see if it will cashflow, and I have a minimum per door I expect from my investments, which can change depending on investment size. 

I understand my net cash flow would effectively be (-) $350 for 18 months in this scenario.Bearing in mind that this is napkin math at this time, is there anything I'm missing that would eliminate a HELOC not being the best overall approach for me?

You want something that's livable but at least ugly, then spend a little money making it more attractive, and you'll be building equity in the property.You're eligible for a VA loan, for with a multifamily, it's a math problem to figure out how much cashflow you'll have coming in and how that will offset the mortgage and other costs.

Do the math re net to you. 

The math problem to solve is: what purchase is going to produce the most equity after the house/duplex/triplex/fourplex is renovated?

But in an extremely high-rent and high-appreciation area like coastal Los Angeles, the math is just isn't the same.Congrats on your investment! 

In order yo be a cash flowing real estate investor, you have to do the math. 

The value of the property then comes down to the capitalization rate from the area which you should be able to get from a reputable broker or by doing your homework on similar properties that have sold

They will most likely expect or at-least chance to get listing from you on the back end.You need to do your own homework but sometimes an experienced agent that works with investors in priceless.   

Weigh the pros and cons of both and do the math to see what makes sense for you.