Best advice is to visit the property, and make sure you get your professionals in there so that you can make a risk based "informed"  decision. 

Our goal is to build a sizeable portfolio to gain financial independence, while teaching our children along the way.

The key is to find a niche, like near that gun range, and to provide a "wow factor", like an in ground pool, game room, near a park, a natural preserve, etc.

I realize the way to protect yourself is to have more equity in the property, but it doesn't make sense to me to have 20% down in LA when I can take that and get multiple properties out of state.

The LLC also needs to obtain an EIN.Your best next step is to speak with a CPA.

My goal is to start paying those down and moving them to an LLC going forward.  

I have a little concern about cashing out enough for a down payment and closing costs on my next house.Do you know how common it is to get a "no-closing cost" cash-out refinance? 

Another relatively easy way to know for sure is to have an appraisal done.

My overall goal is to get started in real estate investing in small rental properties (duplex, triplex, etc.).

@Pat GaraffaSo the plan is to rent it for the long term.If that's so, angering the HOA off the bat with the frankly rinky-dink theatrics you mention might not be the best strategy.