We may have to wait for a handbook update to clarify everything, but the October 6 Frequently Asked Questions seems to be as authoritative a document as anything. Under "Format for Sacrament Meetings", it says:
Sacrament meetings last 60 minutes and are focused on deepening conversion to Heavenly Father and the Lord Jesus Christ and strengthening faith in Them. Allowing the ordinance of the sacrament to be the sacred center of members’ worship on the Sabbath requires careful planning, including minimal announcements and consideration of speakers, hymns, and musical numbers. Ward choirs may participate as local circumstances allow. Sacrament meetings begin and end with a hymn and prayer. A hymn also precedes the blessing of the sacrament.
There's no intermediate hymn mentioned, but there are specific mentions of opening, closing, and sacrament hymns. I would interpret this to mean that as a general rule, there is no intermediate hymn in the new format. Further, I would interpret this to say that if the bishopric decides that a congregational hymn would support the topic of the meeting enough to take that time away from the speakers, that's certainly their right to plan one, but it should only be done after "careful planning... and consideration".
That's just my interpretation, of course. I could be misreading, or the text here could be contradicted by something in the next handbook update. But, I was wondering if anyone else's ward has looked at this and decided specifically not to do intermediate hymns, or alternatively decided that it specifically supports their decision to do an intermediate hymn. Or is it just that every ward's still doing an intermediate hymn because we always have, and no one locally has rethought it yet (the most likely case)?
Again, I don't feel strongly enough about my interpretation to start telling people they aren't supposed to have an intermediate hymn. Of course, if you tell me we're always supposed to stand, or that the music director is the one to tell us whether or not to stand (14.4.3), or call it a "rest hymn", I'll fight you on all of those things.