Have countries with a monopoly on a resource in an area ever established 1-company monopolies in that area to drive up price?
Yes, you are describing the (British) East India Company.  A royal charter granted it a 15 year monopoly on English trade with "all countries east of the Cape of Good Hope and west of the Straits of Magellan".  Also noteworthy, "at the height of its rule in India, the British East India company had a private army of about 260,000 — twice the size of the British Army".