That article doesn't come out and say it, but the ultimate goal of petitioners is to become their deity. Sort of, anyway. See, a petitioner who dies faithfully following their deities' precepts loses their memories, like you've read; What you haven't read is that the memory-less soul that's left has the sole goal of pursuing that deities' philosophy. Eventually, the petitioner comes to understand, embrace and embody that philosophy so completely that they think about and react to things exactly the same way their deity would - and that's the point at which they merge into them.
This means that petitioners of the same Power all have a simple and easy-to-understand goal, and only differ in what they're "missing" to reach it. You could say there's just one question you have to yourself about each player character to determine whether they'll have a motivation to pick up your plot hooks: "Will doing this bring her closer to who she's trying to become?"
You're therefore going to want to pick a Power for the PCs who is broad enough to support a wide variety of classes while still allowing all the PCs to gradually progress towards the same kind of personal ideal. That ideal also has to be compatible with adventuring, so something like a deity of protection or community might be a good bet.
When petitioners go in the dead-book, they're deader-than-dead. As in, the bashers are gone. Forever. No way to bring 'em back. If they're still on the plane they went to when they died, they merge with their deity or plane a little ahead of schedule; If they're on any other plane, the poor sods cease to exist. Oblivion embraces 'em, and whatnot. In other words, no matter what plane a petitioner is on when it shuffles off the post-mortal coil, raise dead and resurrection are off the table.
You might want to modify that for your campaign, or you might not. It's something to think about.
Other than that, the only special rules changes relevant to running an afterlife game are the standard Planescape ones, and rather too extensive to replicate here. They mostly affect magic items and spell casters.
Azuth from FR might be a candidate. He is not a god of magic, but of wizards, and is mostly interested in the structured study of magic. From wikipedia:
The clerics of Azuth teach wisdom and restraint. This means that Azuth is often not the favoured god of sorcerers with their fiery, instinctual use of magic, and bards with their somewhat fanciful approach to it.
From the 3e FR Campaign Setting, the first sentence for Azuthian dogma:
Reason is the best way to approach magic, and magic can be examined and reduced to its component parts through study and meditation.
Likewise, quoting from the Sword Coast Adventurer's Guide (SCAG):
Azuth is god of a wizard's long hours of study, exacting standards of movement and speech, and cramped, ink-stained fingers.
Your cult might have decided that pact magic is an affront to the real teachings of Azuth, essentially a cheat to gain power without real work, swapping sweat with stolen power; without a proper understanding of what is going on. Warlocks could be seen as fools who are endangering the society with their broken understanding. Moreover, since the common folk cannot necessarily distinguish between actual wizards and warlocks, pact magic users will eventually cause serious paranoia within the society against reputable practitioners of magic, ie. wizards, as well.
Also according to SCAG, there are few dedicated centers of Azuth worship, and this fact might play well in your game. While there will be clergy who see this cult as heretics, they will be spread out and might not be able to mount a concerted argument to suppress the cult's "distorted" view of Azuthian principles. (An additional piece of lore information from 2e Faiths and Avatars: 45% of the titled clergy within the church hierarchy used to be wizards. Given that the 5e pantheon is structured in almost the same way as the 2e&3e versions, I don't see any reason if you wanted to keep this ratio also in 5e.)
Finally, Azuth is LN, so the cultists could see themselves as principled saviours who are willing to make the hard decisions others are unable or unwilling to do. What they are doing is to maintain order for the greater good of the society. When witches/warlocks are captured, the cultists might offer them a chance to renounce their pacts, atone for the bad deeds they did under the taint of otherworldly patrons, and start a new life learning magic the proper way. You could even imagine multiclassed warlock/wizards who joined the cult this way and having been converted, they could be even more zealous than the others in the cult.
PS: Following a comment by KorvinStarmast, it might be worth mentioning that within the 5e rules, you might have one or more Arcana clerics of Azuth playing important roles in this cult, either openly or covertly. I can add that such clerics could even be of LE alignment; not only 5e allows it, but also as far back as the 2e, Azuthian church accepted LE clergy according to Faiths & Avatars.
Best Answer
You have no afterlife
Elves in the Forgotten Realms are barred from their afterlife because they betrayed their primary god Corellon by taking set forms, instead of staying flexible shapeshifters like they were intended.
Until he deems it time to forgive them, they are barred from ever entering their afterlive, and instead they reincarnate into new Elven forms after contemplating their failures for a while after death under the guidance of the other Elven gods. This is where the elven 'trance' or 'Remembrance' as they call it comes into play. During a trance, the elf relives events from their own life. But before their adulthood, and after they've reached their elder years, their trances instead allow them to relive their lives in Elven paradise. (Page 36, Mordenkainen's Tome of Foes)
This, of course, creates a strong longing for the Elven paradise, which is where Evermeet comes in. Evermeet is a piece of the Elven heavens that was ripped out of their afterlife by strong elven magic and placed on Faerun. This act nearly destroyed Faerun, and only succeeded because the Elven gods intervened at the last moment to make the ritual succeed.
Evermeet, therefore, is the best next thing you have after actual heaven. Elves who are near death long to go there because it reminds them of a time when their souls were actually allowed into the Elven afterlife. But once they die, their soul is reincarnated into a new Elf.
If you want to truly learn more about Elves, I can recommend Mordenkainen's Tome of Foes. It has a lot of lore about the Elves, their ancient wars and includes the information I've just described in far more detail.