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Wood column with steel flitch plate

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I just wanted a "sanity" check to make sure that I am thinking correctly...
I have a rather tall post that "wants" to be wood, but must be of limited depth and to a lesser degree limited width.  To accomplish that in wood, we are looking at a flitch plate.  I have no problem designing the flitch plate/wood for bending, but there will also be an axial load.  So, I want to make sure that my thinking is on point.  I am thinking that the flitch plate would strictly add to the buckling length calculations (i.e. the Le/d) of the wood portions.  But I cannot quite seem to see an easy way to account for that since in wood it is purely a brace length over depth of member calculation, not a L/r calculation (i.e. calculated section properties).  I was thinking of calculating the transformed area section properties and then figuring out an "equivalent" depth of wood to get similar section properties and then using that "equivalent" depth in the Le/d calculation for the wood.  Or should I just assume that the steel is really taking the axial load and do standard kL/r calculations and assume that the axial load gets transferred from the wood into the steel?  In one direction, it is moot since post is embedded in a wall...thus the weak axis is basically fully is the out of plane length that is the issue.
Or should I go to the Le/(r*sqrt(12)) that is indicated in H.3 of the 2005 NDS for "other column shapes" and use the transformed area value for r?
I am also looking at just using a steel shape with wood nailers, but want to have the flitch plate option available if they REALLY push for it.
Adrian, MI