I use a clone/barrier build. Barrier to keep me from taking damage, and then I give my clone a Hive rocket launcher to kill everything for me. Cryo Infinity headshots to freeze enemies and reset my shield/clone duration to max. Does really well for what I do, namely Slaughter Shaft, Slaughterstar, Heck Hole, and Gigamind farming.
Iām doing a radiation build made for mobs. Doing clone/drone, my clone equips a hive for crazy AOE radiation. Drone set with radiation boost and missiles, and for every enemy affected by radiation they get nerfed and I get buffed. Weapons I have radiation variants of lasersploder, baby maker for reload turrets and handsome jack hammer for the radiation bounce damage on reload, and a radiation hex grenade. So a lot of AOE radiation damage at all times. Shield is red suit to keep me immune to all the radiation going on and an atom balm relic to increase radiation aura and explosions.
Biggest downside is red suit is very low capacity (just over 3k) so heās very glass cannon. Hoping to find atom balm relic with the +1660 to shield to partially counter it. Definitely not the most efficient build out there, and useless on bosses, but I have fun with it.
So exciting! 
I too am in the process of exploring a shotgun-esque Slaughter Shaft build. Mine is based on the Hellwalker and an almost god roll class mod that @kabflash gifted me that boosts shotgun and Jackobs crit damage. I took an earlier variant of the build into the Cistern of Slaughter and it worked well except for the ammo issue that you noted. Then I discovered @Gentlemann on these here forums and his infinite ammo discovery has solved that problem. For my build I donāt actually give the clone a Face Puncher because most of my builds donāt use the clone. But I do use the relic and the Face Puncher myself and after two shots Iām back to max ammo. Then after a brief detour into the menu to switch back my relic Iām back to murderneering.
The Hellwalker was how I got started down this path. It was so fun to shoot. And I was just joking with my co-op partner about how fast I could possibly go while still hitting things. So I got a snowdrift. I was sliding and firing and it actually wrecked a lot of things.
So then I found a Splattergun. And while I wanna find that elusive Snowdrift Splattergun (because it would be hilarious to have all that speed and a slide boost), I think the MM and IB Splatterguns actually do more utility work.
I keep hunting for cool shotguns. The mind Killer should not be slept on. Itās way better than I expected. Itās especially useful in Heck during the Ratch areas.
What is its special gimmick?
Itās a Maliwan Shockwave with no element, and almostt zero charge time
I tried two ways, both lots of fun and effective:
- carrying dome barrier (with augment that staggers enemies), equipping a high fire-rate cryo gun (look for Torgue Blisters or Arctic Star Helix), and staying invincible forever with Calm, Cool, and Collected skill.
- getting 8/5 in playing dirty, plus the capstone that triggers kill skills via action skill, spamming clone and speed+reload boost barrier, and using high caliber, single projectile weapons such as One Pump Chump, Unforgiven, Hunted, Kill oā the Wisp, and a simple torgue rocket launcher for deleting bosses. These guns constantly do double damage this way (more, with torgue stickies).
The One Pump Chump is just a dream weapon, I donāt even really use anything else. You just run around gunslinging and splattering everyone. Great for Duct Tape Mod as well, although for me, the clone throwing grenades is enough.
@Adabiviak Violent violence is +25% damage. Playing dirty is +100%. The COM with +3 to it eliminates RNG, and 5 shots is more than enough for a kill (usually one is enough for a kill), at which point you get another five shots.
Cryo weapons are mostly redundant since he can freeze with any weapon and doesnāt have any buff to elemental damage.
OPC is a great one indeed, any sniper-like weapon does good with PD, I really like Lyuda too since the second shot splits resulting in even more pellets.
I disagree - having the Cyro modifier on top is great, especially for enemies where headshots are a bit trickier. I wouldnāt base my whole loadout on Cryo weapons, though.
The main problem I find is taking advantage of the Cryo - melee synergy. Feels like Iām wasting most of Cryoās benefits if Iām not up in their grill dealing out nasty melee damage. Itās why Iāve shelved my Cold Shoulder - itās hilarious for freezing enemies (two or three shots on most folks - frozen solid) - but that doesnāt actually help me kill them unless I switch to a decently-balanced AR, or another sniper.
IMO most enemies that have tricky crit spots also tend to be armored (Maliwan bots) so itās good to have a back up.
As main weapon, I think fire/rad/shock/neutral to match affinity does better though.
edit: and yes, it sucks that the only benefits from frozen enemies is the melee buff, especially when Zane has zero melee skills. Cryo damage buff relic and being able to score more crits since the targets are frozen is nice too, but should be more.
Maybe frozen enemies should take a severe increase in DoT damage. Give Cold Warrior a reason to exist.
Would make Ice Amara a thing too 
If teammate kills enemies you froze, you should get kill skills up
Non-cryo weapons sometimes kill enemies before they freeze
The goal is to freeze them to keep refreshing the barrier.
I suck and use an infinite ammo, Tediore chuck build. Itās pretty fun but I am looking to respec into a cryo build.
I recently turned him into kind of a radiation monster. I have a relic that gives 13% more radiation damage. I have SNTL do the radiation thing. And I have radiation MIRV grenades. And I have this wonderful legendary radiation beast. I use all radiation weapons, to keep from running out of ammo. I also have a shield that gives some immunity to radiation. In a closed area there is a lot of spillage. With the exception of the shield skills I stay out of the barrier skills.