That's not necessarily true, Adam.
My watch is cal. 353 and has the trapezoidal date window.
The square ones were usually US market versions ("Swiss", not "Swiss Made" on dial). I've never seen a cal. 355 with a square window.
While I think the dials would be interchangeable within the Ref. 2627 with the cal. 353, I don't know if the Ref. 2757 cases for cal. 355 are exactly the same size. So while the dials theoretically should fit the two movements, they may not fit the cases correctly.
Hope this helps,
gatorcpa
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