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Depends on the exact spec of the oil, diesel 10w40 is better than petrol 10w40
Suspect clutch more than gears TBH. Especially if it's related to heat.
Thats why i asked what oil, gearboxes on the 550 are pretty robust, i have heard of ,but not seen, of odd gears breaking dogs off but that dont give false neutrals
It could be the cork parts of the friction discs are swelling with the heat. Could be they are getting real old and this is causing them to swell.