Can stretching my fly line often hurt it in anyway?
I like to stretch mine as much as possible by hooking one end to a fish and pulling. 
(Sorry I just had to)
Really I stretch mine before each use.
I have a couple of older lines that are virtually uncastable until they are given a good stretch. They hold the coils that they acquired on the reel almost perfectly. One good stretch anchored by a friendly tree and the coils disappear. 8T
You had better learn to be a happy camper. You only get one try at this campground and it’s a real short camping season.