How would a cash out refinance work under these circumstances, if at all?

If you're honing a craft, I'd personally like to focus on the one that is going to be relevant in all circumstances and economies. 

I don't know the totality of the circumstances concerning your deal, but if the Seller is prohibiting contractor entry which falls within your inspection period, that's a big red flag to me as an investor AND a contractor.

@Wesley WongUnder NO circumstances would I purchase a property without getting a chance to look at it first unless it was on a foreclosure auction and I would still see all I could see before buying.

I did not hang my license as of yet due to some circumstances but seeing that I will be moving to Orlando for 6 months to do an internship I would love to learn all I can about the area as well as network and potentially partner with some people to get a few deals under my belt.

In my own set of circumstances, I've had to deal with several banks, been told "no" by about 10 banks, had 3 property managers, and a tenant who's just a pain.But, because I had a clear plan and goals on what I was trying to achieve, I'm slowly getting there.  

Those were tough deals and sometimes impossible circumstances and some agents got burned and it impacted their careers.  

In these circumstances, it is better to work with them and allow them to move.

I know your initial investment wasn't one that you would have normally done, but the circumstances permitted you to do so. 

Dog feces indoors, carpet stains, stove looked like it was 50 years of neglect(was brand new).