Thanks for explaining it, I like the solution of the digital clock only running when there is data. Ethernet with TCP/IP is definitely orders of magnitude more complicated than CAN, but both software and hardware is ubiquitous, and you can get modules with UART output for just over $11 from AliExpress. If you want to have some distance between the modules, then running Ethernet cables might be easier. Of course in terms of latency CAN will be far superior, but this struck my as low bandwidth and minimal latency requirements.
Another thing you get for free with Ethernet is galvanic isolation, which can be handy to avoid ground loops.