This is a career change for me, I have been working as a Physician Assistant for 4 years and have been in medicine for over 10 years.

According to HUD, the prescription can come from any "health care professional – e.g., physician, optometrist, psychiatrist, psychologist, physician’s assistant, nurse practitioner, or nurse."

If they sold you the landlocked parcel, they would have been complicit in creating a prescriptive easement across the contiguous owner's land to service your parcel. 

Can I claim a prescriptive easement ?

I am a former Army Officer turned internal medicine physician recently out of residency training looking to get serious about developing my portfolio.

HI David, check with your local Fair Housing office but they just need a letter from a licensed physician.

The problem is that I am a physician getting ready to finish residency training (low cash on hand currently but will make $500K+ in my first year out) and I am in the process of building my own family home, something my wife has anticipated since I was in med school. 

You will have to google physician loans to find who lends in your area. 

Some like investors, some like working with Veterans, some only like to do Jumbo and physician loans etc.

Not knowing what you are going to do with the cash you take out, it's hard to give you a prescriptive answer, so the analysis you should do is when reinvested with the additional amount, does it improve your cash flow collectively or not.