I know you said you already know about the moxxi/grenade combo, but this is what actually works very well. My go to are chain lightnings and a grog. This has been the most reliable method and I’ve used it on all my characters.
It also seems that if you can lead her around the big rock and keep the “just right” distance she will continue to walk without attacking. You can’t get too close or too far from her. I’ve only done this once with Zer0. We just circled the rock while I hit her with the Lady Fist/Bee Combo and she finally died. It does seem that her behavior has changed a bit since the update so this may not be an option.
What you really want to do is kill her ASAP. On my current Axton I’m using the Bee-Hawk/Lady Fist tactic. Unload a round into her skull with the Sandhawk and swap to the Lady Fist before the pellets hits. This takes her down very quick especially if she’s preoccupied with Axton’s turrets.
EDIT: Looks like alot of the stuff that will make this fight easier are available in the Tiny Tina DLC. If you haven’t done it yet you can drop down to op0, complete it, then farm the items at the op level you are at. That will give you at least a 5 level advantage over the enemies in the DLC. You could get the grog, bee shield and chain lightning.