My main concern with this unit is the 4 bedroom/2 full baths.   

My problem with the 3rd (and easiest for the landlord) method is that could end up being quite a few people who don't have a chance of qualifying that end up paying a non-refundable background check etc fee. 

Nope, for the most part you have to look through all the listings like everyone else, but many search methods will let you filter for short sales, and agents can filter for short sales, probate, REOs etc.

Saturation of the market is one concern. 

Concentrate on getting them out, evict when necessary and do not concern yourself with a rent increase.

In NC, the easiest way to accomplish what you are looking to accomplish is to have a long enough DD period to cover your ability to vet your concerns.

My main concern is if I can get a permit the entitlement for a home that currently has a mortgage?

I would be more concerned with the specific deal and the numbers.

I am not more concerned with the profit (low ROI here) but more concerned with if I accounted for everything, or did I underestimate something?

Howdy @Mike TaravellaReally the main concern I would have is not being too leveraged, but, what effect it has on my Cash Flow.