siding weight issues

So we bought all that cement board siding (Hardie Board) for the exterior of 520 rear.  But, after adding continuous (no furrow strips) soundproofing and insulation, the width of the wall is now extended 2-7/8″ past the sheathing, or 3-1/4″ past the studs, which are only 2×4.  What kind of hardware is needed to hang cement board siding that far out from the studs?  Once the calculations are done, the cement board siding comes in at 93 lbs. per 4×8′ area.

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