Yes I understand this is basically all I post but I like the theory and idea ok :D.
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Zane gains increased accuracy whenever he scores a critical hit (20%, not stackable). This decays after a few seconds (3.)
Whenever Zane gains accuracy, he gains increased weapon damage (additive, ~.75% damage per 2% accuracy.) This damage lasts until zane loses accuracy.
This would 1. Give zane a reason for all those accuracy buffs (as no crit damage) and 2. Give him a class mod that actually utilizes his green tree in a meaningful way. This class mod, at full potential, could give zane ~200% more damage. However, I believe this is rounded out by the fact that all of zanes accuracy buffs are situational, with the massive ones needing his shield to be full, not exactly an easy requirement.