My preferred way of changing fly lines whilst in a competition is as you say, reel the while line onto the reel until your top dropper hits the top eye, thread your fly line to the leader/line transition point and re-tie your leader to the new line. Swapping spools at the reel end once the leader is attached. Remembering to thread the line through the line guard if it has one
Using the water to the pull your flies free from the tip (sometimes this doesn't work and manual assistance is needed)
One of tip that will make you change lines more efficiently is having either Cassette reels/spools or spare spools for other reels. Having to change reels each time you swap a fly line can be time consuming especially with cold hands.
Anyone else have something different?