My winning group was:
PLD, RDM, BLM, BLM, BLU/THF, SAM
SAM and BLU/THF would make a Darkness skillchain (Tachi:Gekko to CASA Vertical Cleave) and the BLMs would MB either Blizzard IV or Freeze II. The BLMs didn't really pull much hate, but the BLU did (me). The PLD actually died to Divine Judgment, causing an eventual wipe but it was fine because Alexander does not Regen, even when left alone. So after the wipe we all got out of range until unweakened then we continued the assault. Aside from the unfortunately big Divine Judgment, the RDM and PLD had no trouble keeping the PLD alive.
The goal you should shoot for is getting through part one of the BCNM with no deaths. Alexander is tough defensively and the cures are annoying, but Raubahn is far more dangerous offensively (600+ Circle Blade that wipes shadows to all around, possible 1200+ Seraph Blade, 1100+ Eyes On Me, etc.)