I hope there's a way to export Spotify playlists.
My backout plan is to manually copy over all the artists I'm following. It'll take an hour or two, and I'd have to remember which of their albums I liked the most.
For custom playlists? Currently you're shit out of luck, you'll have to do it manually.
(Horrifyingly crufty playlist backup: https://github.com/rjp/spotify-playlists )
Just grab an auth token from https://developer.spotify.com/web-api/console/get-current-us... and call the above script with it. Very hacky, but it works.