In terms of success...are there any records of a single privateer schooner capturing a convoy of, say, a dozen merchantmen accompanied by a small naval escort (two small sloops)?
Not exactly the case you mention but pretty close. In 1779, Abraham Whipple in command of the Providence
with the Ranger
, commanded by Thomas Simpson, and the Queen of France
by John Peck Rathbun were cruising off the Newfoundland Banks where they found themselves in dense fog in the middle of the 60 ship "Jamaica fleet". The fleet was guarded by a 74 and several frigates. They captured eleven ships without firing a shot. The cargoes sold for over a $1,000,000.
Abraham Whipple had been the captain of the privateer Gamecock
which captured 23 French ships in one six month cruise in the previous war.
Technically, the Providence
and Queen of France
were naval vessels and not a privateers, though the distinctions seem to become blurred. Where is is often said that the line between privateering and piracy is thin (a view I do not necessarily share), in this case the line between the navy and privateering became very thin indeed. A song of the period celebrating their successful cruise, calling them privateers.
"Come listen and I’ll tell you how first I went to sea,
To fight against the British and win our liberty.
We shipped with Captain Whipple who never knew a fear,
The Captain of the Providence, the Yankee privateer.
Chorus: We sailed and we sailed and kept good cheer. For
not a British Frigate could o’er come the privateer."
The Whipple Family blog