Visitor’s Sunday or owner’s Sunday? It seems to be the former as the stated purpose suggests a PSA function and less about reducing owner’s burden in maintaining uptime.

If that’s the case, you could consider using pre-render JavaScript to detect what day it is in the browser. Then temporarily redirect Sunday-identifying browsers to a “Closed On Sunday” page.

It's actually already implemented in javascript, I didn't understand what this was about until I turned js on and saw the blocked screen.