I think I found a solution, and it seems like a very simple one.
There is something called "eCanCrusher". I was a bit sceptical, but decided to download it to my Mac. No installation needed at all, so after unzipping, I just placed the icon on the desktop.
Then I grabbed just one of those epub files from iCloud, and dragged it into eCanCrusher. It immediately created another epub, and this one, unlike before, I was able to open in Calibre. Then copied it to Kobo and voilą...worked like a charm.
Tried another epub from iCloud, and that worked too. Shouldn't be a problem with the rest of them either.
Thank you all for replying.