For some reason I don't have this problem with ctc sounds (when those play, they have no effect on the music channel).
Here is how I've registered my audio channels for ctc and buttons:
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init python:
renpy.music.register_channel("ctc", "sfx", False) #ctc sound channel
renpy.music.register_channel("test_one", "sfx", False) #button channel 1
renpy.music.register_channel("test_two", "sfx", False) #button channel 2
renpy.music.register_channel("test_three", "sfx", False) #button channel 3