The obvious answer is to use a Raspberry Pi as a GPS-disciplined NTP server, of course. Place it near the window or fully outside, depending on GPS signal strength.
That gives you another weekend project, and you can reuse your DIY NTP wall clock!
That never quite solves the auto-timezone/DST issue that OP wants to have work, though, does it?
If I am interpreting their request correctly, they want a wall clock that knows where it is -- and also knows what localtime is in that position on the globe.
GPS (plus some hairy lookup tables) can accomplish that.
That gives you another weekend project, and you can reuse your DIY NTP wall clock!