Yep, it worked!
I removed the day gear, glued on the overlay from a GMT IIc, dial + hands set (two times, now the date changes at 2 minutes before midnight - good enough for me ;-).
But now I've got another problem... the movement + dial combo doesn't fit the case... LOL. That was really a strange EX II I bought there. Now I'd need some kind of distance holder ring so that the dial doesn't connect with the crystal... I think I'm giving up and will sell the parts...
Cheers,
Whatever