Thanks @sdetweil and @KristjanESPERANTO - I solved the problem now successfully using your hints :thumbs_up_light_skin_tone:
Using MMM-Pages indeed looked a bit easier to configure - however, it showed one disadvantage: there were no navigation buttons (to select a page manually or to move left/right, like in MMM-Carousel) - I’d like to have these, because I’m planning to use a touchscreen monitor.
So I went back to MMM-Carousel - and the essential hint was indeed to use the SAME carouselId for ALL same module instances on the SAME page. Actually this is a small flaw in the documentation (the examples there are based on the situation that you have only one instance of a module on a page, and when having another instance on another page, then you need to have a different carouselId).
So thanks again!