GEAR: -Prioritise bonuses to Pistol DMG, Weapon DMG, Jakobs Weapon / Crit DMG
Shield: Re-router for solo, something tankier for co-op (Stop-Gap, Transformer, etc.), anything other than Rough Rider - Band of Sitorak can work, with a bit of tweaking.
Guns: Unforgiven, Bekah, One-Pump Chump (single projectile, high DMG Jakobs guns)
Executor Class Mod - preferably, no Good Misfortune, boost Playing Dirty although VV is nice for Unforgiven
Grenade - It's Piss - damage boost for whole team, bigger gain than the extra 20% off synchonicity with a second action skill
Ice Breaker Relic
Guardian Rank - Overkill, Topped Off - DMG increase, puts cooldown at ~5 seconds
Place Barrier, Piss, Headshot, OHKO most mobs. If they're not dead, they'll be frozen from Brain Freeze and you get extra damage from Ice Breaker. Crit regularly for 50-125k on average with Unforgiven in Mayhem, often goes higher than that. Can drop Annointed in a couple of shots, where other Zane builds can struggle.
Should point out that I got lucky with drops, my Executor gives 41% Jakobs crit and 23% Weapon damage, but this can easily be shifted into a different manufacturer of your choice depending on what bonuses you can get on your items; this can just as easily be shifted into a Launcher / Torgue build, or anything High DMG / low Fire-Rate
When cap raises to 60 - 1 point out of Cool Hand, 5 into Duct Tape Mod to get down the tree, 3 in Pocket Full of Grenades, 3 in Praemunitus or Stiff Upper Lip, depending on preference / gear