Just to add an update to this old thread. (As if one couldn't already guess) you cannot equip Two Two Handed weapons on an Ambidextrous character, nor can you equip a 1 handed weapon with a Two Handed weapon on an Ambidextrous character, and finally you cannot equip a Two Handed weapon with a one handed weapon with an ambidextrous character.
A note for me, since I'm looking to solve the mystery behind two-handedness and at first I thought it would be a range of allowed equips eg. "If you have Avenger equipped you cannot equip any other item 44 or above" But I see now it won't be that simple of a check. They were absolutely thorough with this Two-Handed business, (almost makes it seem like they may have wanted a two-handed weapon for either Edge or Yang at one point since the Ambidextrous two-handed additions are so clean) oy, makes finding out its cause ever the more difficult. It does not appear to be a Compare instruction (all changes of C9 44 did not solve the issue)