I don't really understand your plan, but that's OK. I don't have to. I've offered my advice. Hopefully, you've understood enough of what I've suggested to make it work.
If you're only making your clock 200mm x 200mm, check the cost to do a 200mm x 200mm board. The cost savings of using multiple smaller boards my not be worth the hassle.
Yeah, this is a no-brainer. At JLC, a 200mm x 200mm board is 20 buck for 5 boards. Pay the extra price. I think the chances of your success with multiple boards is pretty slim.
JLC is also doing full-color silk screens. Make a jpg picture of exactly what you want and they will print it on the board. You'll have to read their documentation to see exactly how to do it.
Sorry for the distraction of the multi-board layout. If your design is amenable to being laid out this way and if you completely understand the concept, it's a cool way to achieve a large design cheaply. I think neither of these is true in this case.