If Kirk1 disappears a few seconds before Kirk2 appears, we assume that no subjective experience was lost; a branch of length 0 was terminated. If the transporter had predictive algorithms good enough to put Kirk2 into the exact same state that Kirk1 would be in a few seconds later, then painlessly dematerialized Kirk1, I would have no more problem with it than I do with the original Star Trek transporter.
If Kirk1 disappears a few seconds before Kirk2 appears, we assume that no subjective experience was lost; a branch of length 0 was terminated. If the transporter had predictive algorithms good enough to put Kirk2 into the exact same state that Kirk1 would be in a few seconds later, then painlessly dematerialized Kirk1, I would have no more problem with it than I do with the original Star Trek transporter.