The game is out where I live now, so I think I might as well answer my own question since no-one has given an actual answer yet.
I have done two different battles on showdown demonstrating how Encore works with Z-moves:
Battle 1 Battle 2
As you can see, even when locked into a move with Encore, you can still use a Z-move, and even when locked into a Z-move, the next turn you can use any of your moves, then you get locked into that.
I hope this helps other people too.