Actually, given the Byrne influence on MOS, I'm starting to be tempted to lean more toward bringing in a version of Matrix/Linda Danvers rather than yet another incarnation of Kara Zor-El, so far as this continuity is concerned. Maybe by combining Matrix and the "Superman Lives" version of the Eradicator into a single character - a Kryptonian AI named Kara (hey, it even starts with a "K"...
) - who ends up fusing with a teenage girl, and have her/it be what Brainiac is after.
"My folks came to the U.S. as immigrants, aliens, and became citizens. I was born in Boston, a citizen, went to Hollywood and became an alien."