Selecting a Music Playlist Container as a Stinger or a Transition segment is indeed not possible. However, you can make a Segment with a random track:
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Create a Music Segment
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Create a Music Track in the segment
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Right-click on the Music Track header, and Select Random Step as the type
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For each variation you want, right-click on the Music Track header on the Music Segment Editor, and select Add Sub-Track
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Import the content you want on each of the sub-track variations you created
This segment can then be used as a Music Stinger or a Transition Segment.