Our short term furnished rental property is in an area that has a major medical and research facility.

If it was up to me, the regulation would be very landlord/owner friendly, allowing the owner of a property to lease it however they want (long term, furnished, unfurnished, short term, etc.) as long as they comply with housing rules and establishing punishing mechanisms to the tenant (when doing something against their lease terms) and AirBnb or any other similar platform (when either they do not follow the proper steps to ensure the property is listed by an authorized person or when notified by an owner, they don't take the listing down). 

Todd, "non-residential" generally means that the property is not used to furnish lodging or in connection with the furnishing of lodging. 

Does anyone know of any websites to market this other than Furnished Finder? 

All bills paid partially  furnished  on month to month lease.

Will also suggest that my neighbor drop my tenant a letter (he has been demanding the tenant's contact info, which I have declined to furnish).

Rincon is very seasonal, so in the off season you can even rent for 6 month as a long term furnished rental. 

A travel nurse friend of mine wants to sub-let her furnished apartment in Birmingham to another travel nurse or business executive.Question: how does she protect all parties: her landlord (who is in agreement with this idea), the renter, herself, and her property?

Every Arbitrage deal I complete, that's part of my conversation with the owner/Landlord, and in every deal it's the same response; they don't know STR, they don't know how to do it, how to furnish for it, how to best market for it, the constant over-turn of tenants, coordinating cleaning vendors, active marketing, it's all pain points and while yes they see the revenue potential, it requires an operation they simply don't have commanding knowledge or experience in. 

Just today, Moody's has threatened to reduce the United States credit rating to AA.An article that I just listen to furnish by Keith on another post was even more scary.