This has been a randomly standing request since at least the inception of BL2, if not BL1 (not that there’s anything wrong with that; it’s just interesting how often this comes up organically as an idea).
A new sales pitch to Gearbox for this would be that since the anointment pool was apparently so flooded with options that they actually backed a couple out, if they let us re-roll anointments like this, they could leave them in and be open to adding more if they came up with really fun ones.
Over the years, there have been two paradigms for this that seem fairly popular: straight up retail (where you just pick from a list), but also a grinder option.
Anointment-rerolling Grinder: the weapon you want to revise goes into a primary slot, and the weapon with the anointment you want goes into the second (other two go into the remaining slots). All three donor weapons need to be of the same type and rarity. If the three sacrificial weapons have the same anointment, that anointment is applied to the primary weapon. For each of the other two that don’t have the anointment you want, you need to add X Eridium. The recipes might look like this if you wanted to upgrade a Lyuda with Fire Rate While Sliding to Crit While Airborne:
Primary: Lyuda (Fire Rate While Sliding) + Secondary: Malak’s Bane (Crit While Airborne) + Woodblocker (any) + Monocle (any) + 4X Eridium
Primary: Lyuda (Fire Rate While Sliding) + Secondary: Malak’s Bane (Crit While Airborne) + Woodblocker (Crit While Airborne) + Monocle (any) + 2X Eridium
Primary: Lyuda (Fire Rate While Sliding) + Secondary: Malak’s Bane (Crit While Airborne) + Woodblocker (Crit While Airborne) + Monocle (Crit While Airborne) and no Eridium needed
The idea is to put a limit on time spent farming by allowing the Eridium drops to fund a purchase of the anointment one is after. If luck isn’t on your side, the effort put in still is.
Let’s say you want a Shrieking Devil with a Life Steal anointment. Here’s an example using some totally fake numbers. You tear into the Blinding Banshee ten times and finally get one, but it has the wrong anointment. He has dropped 50 Eridium by this point. You go at him another 10 times; no drop, but you’re at 100 Eridium. Another ten times and you get one, but again with the wrong anointment (now 300 Eridium). Tired of that fight, you run a Takedown and get a Trevonator (wrong anointment) and a Polybius that has the right anointment. Now you’ve got three weapons for the grinder: same type (shotgun) and rarity (Legendary), and at least one has the anointment you’re after. The Takedown run gave you 700 Eridium, so you have a total of 1000.
Now you either need another Legendary shotgun with the anointment you want, or another 1000 Eridium, and you’ll have what you need from the grinder for the Lyuda anointment transfer. Another Takedown? Random world mobbing? Got lucky and got a world drop Butcher with the anointment you’re looking for on the Lyuda?
The maximum combat time to get a weapon with the desired anointment can sort of be capped this way by the Eridium cost. At the minimum, you need an instance of the weapon you want (regardless of anointment), a weapon of the same type/rarity with the desired anointment, and two weapons of the same type/rarity, anointment doesn’t matter. From there, you start grinding. Maybe you get lucky and one drops, so you’re good to go. If not, at worst, you’re only 4X Eridium away from getting there, which you can get anywhere in the game, which also breaks the tedium of farming.