My version was CI and not LL though.
Benefits that i can remember influencing my decision being:
ES on block shield with much more ES aswell and perhaps some damage mod
chaos immune so less resist pressure
Less socket pressure too without 3 extra auras in the shield (i found the socket pressure was pretty hard even as CI)
can get a +1/+1 int/cold level necklace so the damage isn't too hampered (instead of chayula neck)
with rare chest i could get ailment immunity
in essence easier to gear and more defense imo.
I just saw a vid related to this the other day. No idea if it treads some of the same ground you've already gone over, but it might be helpful.
Check it out:
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