That is a good summary Mike. As you note, the 22nd spent a lot of time in garrison duty around New York and later in Rhode Island. The hat companies do not appear to have been in a large number of battles, when compared to the war records of some other British regiments. The grenadier and light companies saw significantly more action due to thier assignment to the consolidated flank battalions, but that follows the pattern for a lot of regiments in the AWI.
Since you mentioned it Mike, I have checked in my new book for information on the fighting around Quakers Hill on August 29, 1778. It appears that in the action, the British 22nd was part of the central column in the attempt to remove the patriot forces from the hill. There isn't a lot of detail, but in general, the battle ended in a virtual draw. The British actually took some ground, but did not accomplish their full objective of removing the Continentals from the area. At the same time, the British suffered more casualties, about 300 to the American's 200 or so.
One interesting element in the battle was an ambush of the 22nd by some men from a Massachusetts' state regiment under a Col. Wade. Wade's men were posted as pickets behind a stone wall, out ahead of the main American line. As the 22nd was approaching American lines, Wade's force rose from behind the wall and gave the 22nd two volleys, before the patriots withdrew. This ambush caused most of the 22nd casualties for the day, which totaled 13 dead and 58 wounded in the course of the entire battle.
The 22nd started the day with about 410 men and were led by a Lt. Col. John Campbell. Campbell had been in charge of the 22nd for a while, having led the regiment in punitive raids against Rhode Island towns in both 1777 and early 1778. His nephew was also killed at his side during the August 29th Battle of Rhode Island.
Noah
Mike