I've started sending the yaw rotation of the player 5 times a second and the snapping has pretty much vanished.
I think I'll end up scaling the update rates with the amount of players in the area with my current settings being the lowest it goes. Although I'm not sure I'll have to, the movement is smooth as silk on the remote systems. First time I've had good movement on games I've tried making... It's been the main thing keeping me from progressing a multiplayer game. Hopefully I can finish this one now.