I’m not trying to attack you or patronise you, I simply wanted to suggest some ways in which your solution could be improved. I don’t understand why you won’t accept the relevance of anything I’ve said. You don’t have to defend what you’ve done, but you appear not to want to improve it either.
Your solution doesn’t improve the accessibility of the widget, it simply solves one problem by creating a different one. You might think it’s less important, but you’re mistaken.
I know your intentions are good, but you’re inadvertently promoting a kind of “ghetto accessibility”. You focus on one group of users (screenreader users), and one solution (visibly hidden) to one problem (undisplaying resets the focus), and in doing so, you end up applying the wrong solution to the wrong problem. Using display was not the issue with the original example; its issue was not managing the focus properly.
There’s nothing wrong with carousels, or with using display:none, if it’s done properly.