I'm not 100% sure about this, but I tested it with Dragonium z and Firium z. Apparently, z moves are always special and never physical.

Tested this with a tapu bulu that has both special and physical dragon and fire moves against a Blissey. The Blissey had 0 IVs in defence with a lowering defence nature and Z-Flare Blitz and Z-Fire Punch both did basically no damage to it.
Same thing happened when I used Z-Dragon Hammer and Z-Dragon Claw.

So.. Z Moves are either always special or they have absurdly low Base Power

Thanks for the report. There's definitely something going on here, although I'm yet to work out exactly what, as there are cases where this isn't the case and the move is definitely physical. We shall look into it further, and if you figure out any more info please comment it here.

It seems as though when the Z move decides if it's physical or special, it then stays as that until you restart your client. I've passed this and what I've found along to our internal tracker.