Nice jacket, btw!
As for the Nautilus, have you by any chance considered the 5800? It is a 38mm time and date only Nautilus which might be perfect for what you have in mind. Not to say that the 5712 isn´t, but just something that addresses the watch size and wearability it appears you are having second thoughts about.
The 5800 has been discontinued for a few years at least, but maybe there are still out there at retailers or NOS in the secondary market.
Congratulations and best of luck in whatever you decide,
Best regards,
Alex

Pic from Google images. 5800 is the one in the far right.