Was there a particular moment between 1763 and 1783 when colonists became "americans" instead of "englishmen" or was it a process?

eh sort of both. before the revolution many people DID come to think of themselves as something other then English, although it wasn't really american it was more southern or northern. Thats also how loyalists came to be, they where people who DID still think of themselves as English. Most people didn't actually think of themselves as American till after the civil war.

Hope this helps!