I'm thinking something like options 1 and 2, but offensive passive feats would be proc'ed through an unconditional special melee attack (with no cooldown), given to pistols by this feat, that works the same as unarmed. Some sort of CQC attack, like in MGS. Straight up letting pistol shots proc combo might be a bit too strong but I think this could be acceptable. Admittedly, I haven't played unarmed yet so I don't know how strong or weak this approach might be but it's sort of naturally balanced by the fact that you still have to get the other feats for it and if it's still too strong/weak you can tweak the damage of this unconditional special attack or the gun skill bonus. Maybe it deals less damage than normal unarmed because it's not a straight hit, or maybe it deals more damage because it's the butt of a pistol and it's hard.
As it stands, you can feel the difference in damage Gun-Fu makes in melee range but I would absolutely trade it for other perks that give me gun damage everywhere if that's all it gives me. Gun-Fu should affirmatively change your playstyle or at least give you more options.