Huh, got Balthier's Fire CSB on the daily. Huuuuge surprise. I was putting on Shiva because I couldn't easily assemble all the parts (dps, CSB, imperil), but now Baltheir will cover CSB *and* imperil, can bring 2 dps's. Looks like I'd better make an honest effort today, which will leave only Valefor, Alexandor, and el Diablor.
EDIT: @SerTabris, glad ya got it figured out! Keep us posted with the progress.
EDIT EDIT: Just beat Shiva a couple times. Once I got the timing right (blind run not so good, sync first not so good, AASB then Sync check) was quite easy.