After reading through all this part of the rulebook again, I believe that it was the wording in the initial paragraph of 29D that might have led me astray:
“At least one player, and possibly more, will have to be dropped to play in a lower score group.”
After reading the subsections, it eventually becomes clear that the player does not actually become part of the lower score group, but I personally think that the way you stated it in your initial reply makes it much more clear (basically, an intermediary score group is formed). Phrases like “dropping down to another score group” seem to be used a few other times in 29D as well.