Bridge cash out is a great option, especially if you cannot access the property bought at auction prior to closing. 

What is the fastes legal action to take in NJ to get access to the rental house? 

I'm a Real Estate Licensee who works in a very remote, fly-in access-only community.

I can see a scenario where I take on the risk of a high interest rate and less flexible terms for 5 years, so I can access my cash sooner if that option is there.

Yours has far easier access. 

- all you would do is "manage the manager", which you could do from anywhere you have internet access.

You could also request it from the agent who quoted that carrier on your behalf since they have access to those carriers / underwriters directly. 

Example a few weeks ago: got a "customized' postcard saying something like "Dear Andrew, we noticed you recently bought a property on 3455 Main Street - we have access to many properties just like this one, all over town.  

But how do I access the funds or profit of LLC for personals use without "commingle business and personal funds" and what the tax consequence is?

Which he's claiming that I'm not able to have access (I think he has removed me from some of our LLCs without my knowledge)(Blind trust is a no go) fighting the banks as I'm fighting for access.