This is an update to my previous post. It seems that my problem was due to the size of the featured images. After having rested them from an average of 2mo to a size and format (jpg at 80% quality) which reduces their weight down to an average of 400ko, my slider works fine. I don’t know if this has to do with a limit to how much data the slideshow scripts can manage, or a limit imposed my ISP, but evidently size matters !
Hope this testimony helps others out there.