I've been wondering if we could pretend that this is an alternate timeline where everyone's gametes combined just a bit differently, explaining their different faces and voices. That's actually quite credible; the same procreative act, if it happens twice, would almost certainly lead to different combinations of sperm and egg, so the different versions of the "same" person should be non-identical. However, there's too much precedent of alternate-timeline copies who are identical to the originals, so it'd be hard to justify an exception.
I love how hard you try to come up with reasons to explain everything, but I think this might be pushing it just a little.
I know, but it's fun to play with ideas.
And there is a bit of precedent in
Sliders. In that series, the characters travelled among parallel timelines and constantly met their own doubles (who, by an amazing coincidence, were usually the most important people in the whole world). Once, the hero Quinn Mallory met a "double" who was the female version of himself, born with two X chromosomes instead of a Y (played by the actress who was later Tal Celes on
Voyager, IIRC); and in the final season when the lead actor left, Quinn was replaced with a "fraternal twin" double, a child of the same parents but with a different genome.