Would need a new movement.
But, there are a lot of things that can be done without physical move the window.
You can make it appear to be moved…
NOTE!
I love this watch and I think JLC have done a fantastic work while creating this one!
I don’t want to start any rumour of different versions and so on, so my examples are very ruff, no one should be able by mistake take them for real!
With that said – like always when it comes to design, it’s a matter of taste.
1. Original dial.
Example;
2. Take away the frame around the date window.
3. Keep the frame but move the alarm ring marks closer to the alarm disk.
4. Take away the frame around the date window and move the alarm ring marks closer to the alarm disk.

Best
Blomman