Besides selling the property (which I REALLY don't want to do) is there any other way to access some of that equity?

What makes appraisals better today than they ever have been despite these monumental flaws, is that appraisers have access to more data than ever before, the most relevant and significant of that are the interior photos of comparable properties that agents love to post on the MLS.

My reasoning - my cash can constantly be at work in the aforementioned portfolio (as opposed to a money market type of account), but I still have access to 60-70% of the cash to continue flipping a couple houses at time.  

Running a profitable business is one of the hardest things out there and letting someone have access to that can severely limit your upside potential.With the likely volatility in the stock market, real estate and notes will be attractive options.

An independent agent with access to Travelers will most likely be able to write you the type of policy you need.

Regardless of the new layout, I know there are people in here with access to the type of deals I'm currently seeking. 

Decide how much money you have access to, & the zip codes, city or state you want to focus on.

Also, you make it harder for yourself to access cash when you might need it, whether for emergencies or more investing.I'd go the other way. 

Is access easy where you do not have to turn around in a median to get there?

Just getting access is hard enough, then when you finally get it, you wish you hadn't.