Actually, there's a solution:
1. Turn off the Watch
2. Forget the 2.4Ghz and 5Ghz Wi-Fi connections on the iPhone
3. Turn off Bluetooth on the iPhone
3. Connect the iPhone to the 2.4Ghz network, and then turn on Bluetooth
4. Turn on the Watch (this caused the watch to connect with the iPhone and connect to the 2.4Ghz network using the iPhone credentials)
5. Turn off Bluetooth on the iPhone and then test that Siri still works on the Watch or send an iMessage, etc
6. Turn Bluetooth back on on the iPhone
7. Disconnect/forget the 2.4Ghz network on the iPhone and connect it to 5Ghz network
8. Check again that with Bluetooth on iPhone turned off, Siri/iMessage/etc still works on watch and Watch MAC address appears in router attached devices list (it only appears when Bluetooth on iPhone switched off).
The key thing seems to be to first connect the Watch with the iPhone when the iPhone is connected to the 2.4Ghz network, because the Watch does not connect at 5Ghz (only 802.11b/g/n 2.4GHz Wi-Fi) and will only connect to a network that it has learned from the iPhone. After that, the iPhone can be connected to the 5Ghz network.