I deal with those radio systems occasionally and I've always wanted to find or modify a digital watch to display the Julian date. It feels like that would be such a simple firmware change to something like a g-shock.
Check out the Sensor Watch project[1]! It's "An ARM Cortex M0+ board swap for the classic Casio F-91W wristwatch" that allows you to write custom firmware.
[1]: https://www.sensorwatch.net/