Handsome Sorceror has the same loot pool as the Warrior, the main quality drop is the Conference Call but you’re not likely to get anything else great from him. However, in that level are many chests with could drop you a useful Monk class mod, like a Chaotic Evil Monk or anything with +6 Money Shot.
Your gear is underleveld which is probably why you are struggling a bit. I’d look for an on-level Harold from Torgue farming or Savage Lee. Grog level doesn’t matter of course. If you wanted the Deputy build, there’s a list of useable items there and where to farm them. @Chuck80 is one of the most knowledgeable Sal players around, so definitely read his guides on that build. It works at all levels. I suggest slag grenades and you need something better than that terrible Lightning Bolt anyway. Since you’re at Dragon Keep, if you kill the first two enemies right in front of you when you spawn in, it spawns a Badass wizard that can drop x2 or if you’re lucky, x4 magic missiles. There’s other places to farm those to, but that’s my spot. A slag transfusion, bouncing Betty, or singularity grenade from a world source like the Snowman Chest all work. I like grenades to slag, guns to kill, though with Sal, you can also use singularity grenades as crowd control and use a grog or slagga in the offhand to slag, so maybe it’s less critical to use slag grenades with him.
In terms of getting you that Leg Gunzerker mod, that’s a tough get. I’d look on the Sal forums for normal class mods that are good until you can get one. His most common leg mod, the Leg Beserker just isn’t good unfortunately. You can only get a Leg Gunzerker or Leg Hoarders from Tubbies, which are annoying to spawn and have a big loot pool. That said, behind Ellie’s place in the Dust or Caustic Caverns are good places to farm. If you have a friend, take them, because more players means badasses are more likely to spawn and every time the game spawns a badass, it has a chance of being a Tubby. Therefore, you want to go somewhere that spawns a lot quickly, hence why Spiderants and Varkids are a good tubby source. The True Neutral and Chaotic Evil Monk mods you can get from Tiny Tina are boss killer mods, with the +6 Money Shot, but I don’t think they’re the best for mobbing.
For Shields, I like Adaptive shields for Sal, so the top tier of that list is the Evolution or Neogenator, but I wouldn’t farm for something you’ll outlevel soon anyway, so see if you can get a decent blue or purple adaptive shield as a world drop. The bee is good with him too, as long as you accept it will be down most of the time. I’m a fan of absorb shields in general, but again with Sal, your shield is down so often…that’s why I like Adaptive shields because you still get a boost. I would farm for a Rough Rider at some point, as that will be useful with the Money Shot builds around your CEM or TNM class mods. It drops from Bulwark in the first level of the Hammerlock DLC. I think you have to take that side quest, just look it up on the wiki, it’s not too hard.