It also seems that, if each kilometer is thought of as expanding over a period of time, wouldn't much of the expansion between us and the other star be happening behind the light as it traveled? To my mind, this means that any light we're seeing didn't actually travel the entire distance from there to here.
I think it's the opposite. The expansion behind the light doesn't affect the light itself, so we don't see it. The expansion in front of the light, however, makes it travel longer than it would have to without any expansion, meaning the star was closer when the light was released than the total distance the light actually has to travel to reach us.
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