I'm also using a Sony Z5 and the last couple of days, after I updated to fw 3.30 and did the "update bluetooth connection" in GC mobile, the music controls have been working flawlessly. Before that it was a hit or a miss with the controls, as it was with the fr235 and the Z5, so I'm hoping the last few days hasn't been just random lucky.
Can I ask what you mean by "update Bluetooth Connection" in the Garmin Connect app?
Thanks