Hi @7675t
Sorry for silence, I wan enjoying holidays without internet 
Anyway I have checked and made some changes to my example snaps. And we are very close to make this use case also work.
So install latest avahi and avahi-client from --edge channel and connect all needed interfaces.
$ snap connect avahi-client:avahi-control avahi; snap connect avahi-client:avahi-observe avahi; snap connect avahi-client:network-observe core
For your testing you will need to, for the moment, bind mount one file
$ sudo mount -o bind /snap/avahi-client/current/nsswitch.conf /etc/nsswitch.conf
Now you should be able to run:
$ sudo avahi-client.ping <something.local>
To get this working properly you need to follow landing of this feature: layouts-re-mapping-snap-directories
Once this lands you will be able to add to your snapcraft.yaml
layouts: /etc/nsswitch.conf: bind-file: $SNAP/nsswitch.conf
this will create impression for file overlay only inside the snap context without affecting rest of the system, without need to run that manual bind mount