Ok, we tested connecting Emote to an H9000 on a Mac running Mojave with the latest version of Emote posted on our website (v18.104.22.168) and the latest H9000 software (v22.214.171.124). Everything was working fine. So, I don't think the problem you've been experiencing has anything to do with Mojave.
Would you mind double checking that you are running those same version numbers as well? On the H9000 the SETUP page will tell you which version number you have installed, and in Emote hovering your mouse over the Eventide icon in the bottom bar will show you which version you have installed.
But assuming you have the same versions installed as I, it would be nice to verify that the IP address you are seeing in your H9000 is a valid IP address. Could you open up the Terminal app (under /Applications/Utiltiies) and ping the IP address of your H9000? In one of the screenshots above you showed the IP address as 192.168.0.37. So, you'd type: ping 192.168.0.37
If it's reachable, you should see something like this:
PING 192.168.0.37 (192.168.0.37): 56 data bytes
64 bytes from 192.168.0.37: icmp_seq=0 ttl=64 time=0.711 ms
64 bytes from 192.168.0.37: icmp_seq=1 ttl=64 time=0.779 ms
You can press CTRL-C to stop the pinging.
Or alternatively, if it's not really inconvenient, could you try connecting your H9000 with ethernet instead of WiFi?