So during decoherence you don’t have classical worlds - the probabilities interfere so you can’t ignore the other terms. Over time that interference reduces, but as you say never disappears completely.

But at no point does one world even approximately emerge - it’s always many. I can say only the one I experience is real, but there’s no justification for it.

Your main problem though is thinking classically - you can't justify your theory by saying it can be reduced (after an infinite amount of time) to an old way of thinking. Classical probability is fraught with issues; just saying it’s always been acceptable isn’t true nor a rational argument.