To be honest I don’t think remote viewer software is ever going to be the best solution for this. Particularly with an active screen display, it’s going to put a fair bit of load that you really would be best of avoiding.
Without digging into it more, I can’t really say what might be causing this, but another interesting experiment might be to enable TightVNC, but minimize Cantabile’s main window and see if the glitches still occur. In this configuration, vnc will still be running, but the screen updates won’t be sent across the network. Just curious what happens in that case.
The other thing you could try is disabling Cantabile’s multi-core (or at least dropping the audio thread count by one). This might free up a processor to help service the network layer and prevent interruptions on the audio thread. Just a guess.
As for the best way to remotely control Cantabile, I think via something designed for that exact purpose and is the motivation for a network server API. Whether that ends up as a dedicated remote app, or simply the ability to point a web browser at Cantabile I’m not sure yet.