To leverage the equity for financing my next deal, a second mortgage seems like a more cost-effective option.

(This option would would not carry any debt, all debt would be paid in cash)Or keep our current house, rent it out, and cash flow NET monthly about $1,500?

However, there are some investors here who are having a lot of success finding cash-flowing deals through off-market sources. 

Is there a month-to-month option?

I know that the regulations in Beverly Hills is "friendlier" to landlords than Los Angeles and I'm exploring the option to convert a multifamily apartment into condos. 

Quote from @Samuel Pavlovcik: @Nicolas Tow Your Architect is correct that it sounds like the only option for you would be to obtain a Zoning Map Amendment to change to RT3.5 or higher.

I think the economy has a number of diverse employment options, lower prices than King County while still being within driving distance.  

I am looking at different loan options but to break even (not having to put any money of my own in the house after the initial down payment) the current down payment required is that much. 

Typically, the investors I work with purchase properties in their personal names and then quit-claim the title into their LLC after the deed has been recorded.Markets like OKC, Memphis, and Little Rock offer some excellent, affordable growth opportunities, and I’d be happy to chat with you to explore these options further.

With a family and kids the best house hack is a house and cottage or duplex option.