Hi,
Thank you very much for the details, it helps us a lot!
I found that the playlist posts stores the actual shortcode with the “playlist_shortcode” custom field, not in the actual post content. Then, on the index table option panel I added that custom field, and re-indexed everything. The keyword count went up from 1308 to 1532, so I am guessing that some more content is indexed now – hopefully the contents of the shortcode.