Maybe it eas beginners luck, but I managed to change the belt, clean and lubricate everything inclusing the motor - and everything works!
Also managed to clean the Beocord and change the belts, so that’s also working again.
Now I just have to check the DIN-plug for the Beogram, as it has a loose connection - then everything is good as new. Well, almost. Thanks for your detalied description :)