The Soundiiz service offers a number of features for moving playlists between different music streaming services. One of the challenges in this domain is matching song titles, artists and track information so that the song you listen to on one platform is actually the same song linked when the playlist is created on another platform. There's no common identifier for music tracks or albums (like ISBN for books) so the problem of matching is why it's hard for you to simply export your playlists on one service and load them into a different service - not only the playlist export format but also the track identifiers are likely to be non-interoperable.
Playlists can be copied one-time to another service, and Soundiiz also supports synchronizing. There are other features around sharing that might be useful too.
Some ways this might not work for you:
The source code (markdown) for this article can be found on GitHub.