The seller has already come down a lot from my initial offer due to unforeseen problems during the inspection. 

Might make sense to use the inspection contingency to stop the deal since lots of unforeseen things needing rehab popped up during it.

Doing rehabs professionally for many years the best advice I can give you is to simply try to take your emotions out of the deal, and ensure you have enough reserves to cover all the variables that inherently always go wrong like unforeseen rehab, longer holding periods, etc. 

I am thinking about: Charlotte  or Raleigh/Durham4) How much should I budget for acquiring location, furnish it, and for unforeseen circumstances?

If none of that could work I would just ask myself if the unforeseen worst case scenario happens do I have adequate wiggle room in the budget?

It does require some confidence on your end to know what you are doing, how much things cost, and build in some contingency (the oh %€£ budget) for the unforeseen things that will arise. 

A HML usually wants to know your track record and if you have enough money to finish the project, and enough for carrying costs, and unforeseen events, and then they will lend you according to what they feel comfortable with.  

Renovation costs ballooned 50K over budget due to unforeseen that came up in reno and our adjustments to off-set, which I did manage to increase our ARV 75K from original projected and we did exit at full profit points.

With anything in life, unforeseen circumstances happen, but maybe with presumably solid home and solid tenant screening you won’t have those large expenses in the first few years?

No rational person could hold you accountable for the unforeseen if your and their due diligence was thorough.The best way you can maintain the relationship is to provide them more properties that will (presumably) make them money.