... about vintage watches on this site! Very interesting facts about that Grande Complication and the signing of the movement indeed.
The watch is not only featured in the Book of Timepieces as one of 7 wonders but also in Mr. Cologni's Better Book of Timepieces. Sadly none of the books contains the information you provided. That may be neglectable for the Book of Timepieces but not for Cologni's massively overestimated book. Cologni allegedly undertook a lot of research for the book - I wonder where all these efforts went: they do not materialise in the book. Not for the featured Grande Complication and not for most of the other vintage (or better: not currently produced) pieces. Concerning the signing of movements: Cologni shows watches signed LeCoultre on the dial next to the seemingly fitting movements signed Jaeger-LeCoultre and vice versa. One could get the impression that he is not even aware of what's behind the different signing.
Christian