I have a book "Ontario People 1796-1803 which is a transcription of the original record of names of those who qualified as Loyalists that is in the National Archives of Canada. There are no Kline's listed in the index. There are 3 Clines, George, John and Michael...John and George are Michaels sons. The Eastern District (formerly Lunenburg) comprised all of what is now Ontario between the Ottawa and St. Lawrence Rivers from the current Quebec boundary to a line running due North from approximately Ganoque?, Ontario (just west of Brockville) on the St. Lawrence River. The dates you give for Philip and Anna are earlier so they may have left Canada before the American Resulution ended?