Congrats on the Dante upgrade! If the H9000 is the only Dante device in your setup, you’ll want to check out Dante Virtual Soundcard: https://www.audinate.com/products/software/dante-virtual-soundcard
The Dante expansion card can work as a network switch, allowing you to still use a single ethernet cable connected directly to your computer. Connect a short cable from the H9000’s ethernet port to one of the Dante primary ports, and connect the other primary port directly to your computer. Now you can connect to Emote and also access the Dante card’s I/O.
In Dante Controller, make sure the Dante card is set to “switched” mode: https://dev.audinate.com/GA/dante-controller/userguide/webhelp/content/network_config_tab.htm