Your reviews on the subject are a beauty to go through. I never realised that JLC made a Reverso minute repeater! All of the watches in the collection are phenomenal! Jaeger le Coultre should do a Patek and construct a museum of some kind, particularly one dedicated to Reversos!
While on the subject when does their patent run out on the Reverso model design? I have seen early C20th watches with similar attributes, and do feel worried that the design may be open, one day, to legitimate copies/variations by other watch houses.