How can I enable the Yatse remote interface?

Seems you changed the webinterface and also the port. Not sure if both of it was on purpose. Default should look like

osmc@osmc:~$ cat .kodi/userdata/guisettings.xml | grep web
        <webserver default="true">true</webserver>
        <webserverpassword>osmc</webserverpassword>
        <webserverport default="true">8080</webserverport>
        <webserverusername>osmc</webserverusername>
        <webskin default="true">webinterface.default</webskin>

You can leave the port on 80 if you want. But suggest to change the webinterface to default to avoid issues.

Also ensure that you have these three settings on true
<services> <esallinterfaces>true</esallinterfaces> <webserver>true</webserver> <zeroconf>true</zeroconf> </services>

If all to no avail than go the vnc path