I know you would like this piece quite easily. The price is not set to be liked by us oldtimers though. The numbers on the price tag is rather scary, at slightly "above" the Moonwatch Caliber 1863.
The recessed date correction button I think is not an aesthetic choice but was necessitated by the nature of that movement design. I wish I had more information on this movement but it appears to be quite elusive. But to address your concern, no, the sportiness of the watch was not affected because you will have to try to look for that button. It is nearly impossible to see once on the wrist.
Ruckdee
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