I’m surprised that you have to reroute everything after rebooting the H9000. It should retain its current state through reboots, unless you explicitly clear the current state with a soft reset.
Like Puppeteer said, try Emote > menubar > Session > Save To H9000 after you’ve set up the routing. You can then double-click the saved Session in Emote’s sidebar to reload the Session.
If you use Emote as a plugin in Logic instead of as a standalone app then Emote’s state will be saved along with Logic’s project, and you’ll be prompted to restore Emote’s state when reopening the project, which could be of use. Saving Sessions is definitely best practice, though.
If your computer’s connected to the internet via Ethernet, then you can probably just connect the Dante card to the same router that your computer’s connected to, unless that router uses EEE.
Let me know if that helps.