1/ No, JLC doesn't have a round manual movement with a centrale second, except the Duometre...
2/ There must be some NOS movements, but in too low quantity for even a short production.
Now, you raise an important question: JLC can, or could have found a manual winding solution to this question. They are JLC, the Watchmaker's watchmakers.
Them, without counting the price they will sell it, the Watch lovers without counting the price they will pay.
With one question; though... Will people be ready to pay more for that iteration than for a excellent vintage one?
Food for thought...
Best, my friend,.
Nicolas