My two bits is a new piston and rings.
I would be reluctant to try wider rings, getting the gap / clearance / gas pressure correct to seal the rings is close to rocket science. My Morini 500 had custom rings fit from some kind of fork lift engine, previous owner meant well but the machining of the piston grooves / bigger rings resulted in 80 ~ 85 psi per cylinder. The rings fit the cylinder but the gap / clearance etc was all wrong. I had to get LA Sleeve to resleeve the cylinders and fit stock pistons and rings.
I read an article in Classic Bike Guide by Richard Rosenthal on the subject and it left me of the opinion that stock designs of pistons and rings is critical to good running.