Sounds good. Better yet, don’t get killed. Just hit the safe chests for now
I like the one in Tundra Express for non-combat farming of standard gear (the drop-off by Madame von Bartlesby’s area).
Gaige can be a bit tricky to farm for since several of her weapons of choice which aren’t in the unique category are just annoyingly hard to find, world drops being what they are.
One gun which is amazing on her but involves a bit more running about is the Blockhead from the Caustic Caverns. Just bolt it till you get the drop. With that gun in hand you’ll never fear a Bullymong again - in fact, most flesh enemies will regret ever picking a fight with you.
Remember that although Jakobs shotties are great for raw damage, anarchy loves grenade splash and the Blockhead has plenty of that. (There’s a reason that gun is amazing for Axton and Krieg as well.) Conversely, Gaige has no crit damage bonuses outside one line of COMs.
I agree with @Adabiviak that your COM isn’t the best one going, but it’s not bad for general purposes. A good Pangolin shield should do great, it’ll keep you alive while you farm Tubbies for the Leg Anarchist and Catalyst COMs, both of which are amazing.
If you can get an offensive shield for DT you’ll be well ahead, swapping after summon can be a tad annoying at first but you’ll soon do it so quickly you don’t even notice.
Once you’re a bit better geared I agree with @ChemicalConundrum that a UVHM reset to acquire things like the Pimpernel and Fibber could be worthwhile, not to mention the Hail.
On OP0, that’s still a raid-killer for Gaige. The Pimpernel is of course absolute murder and the Fibber is something you’ll get tired of pretty soon due to how OP it is.
I don’t really see any problems with either of the suggested builds, although one or two people may remember me not being a fan of Close Enough because of complicated and partly irrational reasons which you can safely ignore (apart from the points expenditure - IMO they can be better used elsewhere.)
The only things I’d advise you to do is to max out Unstoppable Force for the mobility and DOT-defeating shield regen. It’s a bit like Grim, Followthrough and Quick Charge in one.
Your points in MoSS aren’t really helping you much without a Blockade, with the important caveat that one single point grants much more DR against fire damage than it actually ought to.
(According to forum rules I’m not allowed to tell you how I know that, just roll with it.)
The second part would be to avoid Buck Up outside specific scenarios like raids. It can be very helpful there, but while mobbing it distracts DT from killing stuff and you have some of the best shield skills in the game anyway.
The points in PaaP are a bit meh, on the whole I’d free those and the MoSS ones (except for the single one mentioned above) toward the LBT tree once UF has been maxed. On the whole, Tiers 3 and 4 of the LBT tree have some amazing skills to synergize with elemental damage, splash damage and all related ways to make people miserable, especially when you find a Leg Catalyst.
You can build for that already, but of course even more so at 72.
You’ll have a bit of a grind getting that gear, but the journey from being horrified to becoming horrifying is probably worth it.