The trilemma is a spook. A is the only sensible choice, because having any kind of monetary policy besides "we have a currency, X units of it is worth Y of [resource]" fucks a nation in the long run.
>Is it possible to have a privately funded country that doesn't have it's own currency?
Yes, because states aren't the only entities capable of maintaining a currency. In a free market, banks would issue their own currency, backed by their own reserves of gold, silver, or whatever real-valued asset is most beneficial to them. There would be a market incentive for banks to accept the notes of their competitors, because it increases efficiency.