In principle, the Raspberry Pi compute module is the thing you're supposed to use to embed into projects like the clock. I've done a little bit of looking at it, and in theory it is possible to design a board that would accept a compute module instead of a pi zero w. There are a couple of fairly big problems with the idea, however.

• The compute modules are very expensive compared to a zero. The CM3 is actually the same price as a Pi 3B while being far less capable (at least without breaking out a whole lot of connectors and stuff).
• The clock would need to supply 3 different voltages to the CM.
• It would need to have a USB connector and would need some special circuitry to allow the special USB bootstrapping to initialize the on-board flash (you could initialize the CM separately and not include that support on the clock, but that makes it a whole lot less maintainable by the end-users if, say, they have to replace their CM). Adding a OTG capable USB port would be necessary in any event for either wireless or wired networking.
• It remains to be seen if an equivalent 40 (or 26) pin GPIO header could be added to the clock to support traditional expansion. How that could be made to fit would be the next big question.

The nice thing about such a beast is that (with the CM3) it would have the same CPU performance as a Pi 3, but the actual benefit of that for the purpose of the clock is questionable at best.