Some Kawasaki twins have experienced issues with the valves dropping into the valve seats, which may explain the ever-increasing valve clearances.
To break a rocker I would expect that you would need to contact the piston with the valve.
This is what happened when the cam timing slips and a valve contacts the piston on our CRF150R -
I'd check the cam timing and also take a look at the top of the piston if you can.
I wouldn't run a 10W-50 oil. I'd run a synthetic 5W or 10W-40. There may have been some oil-related issues in the past if the cam was chewed-up, though you can see our cam got messed-up due to the other damage.