What are the rise in meetings a symptom of? Are people using meetings to replace walking to someone's desk, or are they using meetings as a measurement of control/participation?
I've also found ~medium success with heads down/quiet hours, something like 10-12 and 3-5. Conversations/meetings/whatever have to happen outside of quiet hours because quiet hours are guaranteed productive time.
https://products.arkency.com/async-remote/
Might be worthwhile looking at. (Not associated with authors at all)
Also I found this article how Doist is doing async work really good:
Decisions, tickets, etc.
Completely async and transparent. (Of course, require discipline and writing)