So in looking at the two-page spread of the new Fortress of Solitude in last week's Action Comics Annual #10, I noticed that there are statues of the old (pre-Crisis/ZH/Reboot) Legion of Super-Heroes in there, not the current LoSH.
Which led me to a realization: The current Supergirl and The Legion of Super-Heroes comic is probably set not in the future of 'New Earth' (i.e. the current DCU), but rather in the future of the 'New Parallel Earth' (or whatever they end up calling it) that is being hinted at.
This would explain why the Supergirl in SatLoSH is different than the one appearing in the modern day DCU. I also seem to recall some multiversing going on in the final issue of the old Legion when the new LoSH was introduced.