Hello Arnaud, your problem is common problem. There are worn gears. Also you have too much free play of bearings. They should be tight in position. Their position should be on their stop in position in casing, so I think it's more inwards. You should put new bearings and use loctite bearing loc. Also you need new gears, you have worn third gear inside. Gears aren't problem to get here, older, but good. Also I can recommend new shifting forks and springs in mechanism. It's also commont problem of older JAWA.