I don't know how playlists work but would this work?
Create Playlist A with the desired songs in the desired playlist order.
Create Playlist A-1 with same songs shuffled.
Create Playlist A-2 with same songs reshuffled.
Create Playlist A-3 with same songs reshuffled again.
Then if you want a shuffled order you can just pick a different shuffled playlist so you aren't always listening to the same order?
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