Michael, you just beat me to it.

As someone who plays a concertina, I would call myself a concertinist (when playing concertina that is). When playing recorder I would add "player" rather than use recorderist or recordist as the first is clumsy and the second is normally applied to someone who makes recordings.

Of course violist doesn't work for someone who plays violin because it is the name for someone who plays a different instrument, namely the viol.

Otherwise I entirely agree with what you say but would add that it can also be a matter of context as with the recorder example above.