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.
My current house, with low-E windows, aluminum siding, and a metal roof? It passionately hates everything about GPS.
But in more-typical (stick-framed, asphalt shingled, vinyl-sided, US-ish) houses? I haven't had any trouble with my very inexpensive u-blox (or perhaps clone) GPS board, a presumed-decent GPS antenna that we were throwing away at work, and dainty little [IIRC] u.FL to SMA adapter to connect the antenna with. (I put this all together just to play with making a GPS-backed, low-stratum NTP server -- which was a much more-rewarding process than it had any right to be.)
It was bizarrely good, in fact: While it certainly saw more birds and presumably had better accuracy when sitting in a window, I had real trouble getting it to cease to operate. It seemed to lock on well-enough to provide time and PPS until I put the antenna into a windowless closet.
That said: The antenna that came with this cheap receiver was trash -- at best, 1/10. It was hard to make it work even outdoors on a clear day. I eventually got sick of looking at that part and binned it.
