Pip wants to play more than one note at a time, but without committing to piano.

Accordion group - acc., concertina, melodeon
Hammered dulcimer - if you like the sound
Mountain dulcimer - don't just strum it

I'm proud of my mountain dulcimer playing, but I have the advantage of piano lessons, music theory and experience with finger-picking guitar.

Pip, I see that you have a zither. Have you considered becoming more accomplished on the zither?