Well im no expert at this because i have never tried it myself, but technically you should be able to get Mira on LS, then turn towards DS. What I would say to do is stay on LS (even if only a little), then as soon as you get Mira, go full on DS .
P.S. not sure but I think in Nar Shaddaa you cannot leave till the end of the quests are completed
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but you can still be neutral and get her then it would be easier.