Even if the Norfleet is not buffed by grenade damage it is still the most powerful rocket launcher in the game and you can just slap on an elemental relic that matches the Norfleet. Being an E-tech the Norfleet ignores cover when the rounds detonate, enabling it to kill enemies regardless if they are behind a wall or not but this also goes for the wielder as well.
I would stay away from the Antagonist shield. I used to love it but it has a habit of slagging you if you are struck while standing behind waist high cover and the slag orbs have a very low chance of slagging. You can either use the Blockade as Khimerakiller mentioned or if you want to replenish your grenades and rockets without relying on ammunition drops the Big Boom Blaster shield should be considered as the boosters it drops give one grenade and one rocket each.
If you want to carpet bomb entire areas with grenades get either the Bonus Package or the Shooting Star. The Shooting Star has more risk involved but if you toss into a confined space full enemies it will do a lot of damage. Or if you’re struggling with slagging either the 2x or 4x magic missiles will work and also make it easier to get out of FFYL if you have Do or Die. Not saying the Fast Ball is bad (there are videos out there of Axton players one-shotting everything with it) just throwing more options out there for you.
If you want to have a more “Quick and the Dead” setup use a Legendary Ranger instead and just move some skills around to get the most out of it when the kills start rolling in. Granted with the Legendary Ranger COM you develop a glass jaw but you can also bulldoze enemies left and right.
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If you’re not in danger of dying a lot, go with the extra damage.