There is a thread “PMSM motor Modeling” (PMSM motor modelling) where @bordodynov tells about his LTSpice model collection. I found exactly this model (under “Motors\Ind3phMotor” but for LTSpice), and it is working. I didn’t find any differences that matter for my problem with the “mutual coupling”.
Here is a screenshot of the motor model:
So maybe there is someone who finds the problem in my model.