Try this:
sudo systemctl stop tvheadend
rm ~/.hts/tvheadend/input/linuxdvb/adapters/*
sudo systemctl start tvheadend
Now log in to the TVH webui, find the tvadapters page again, enable only the sony tuner, attach to it the network which has your local muxes, and hit Save.
After a while, you should get some channels showing up.
Full story here: Watching live TV with a USB DVB tuner or network TV tuner