In the past, I've developed histories, theologies, and factions with a combination of Microscope and Kingdom.
In the living history I've developed, you can see the records of a game of Microscope which developed the history of the world, and a game of Kingdom, which detailed the factions and history of one of the local towns they lived in. By setting givens of the character races of the D&D world and some other generalized "this is how my world is." I made a far richer history than I would otherwise have been capable of.
To do this properly, I would have players engage in this world building before character creation, and then employ my methodology at the end of this paper. While the group character creation process is alien at first, it flows naturally from the group history and group politics and allows for remarkably nuanced and well-rounded characters. Obviously in a game like 4e, the group character creation can only really impose narrative requirements. The mechanics of the characters can be left to the people of the group who enjoy that sort of thing.
It has been a long time since I played Vampire, but - not only is it possible to do a group creation followed by individual preludes - it's the best way to do it.
You will probably need to have a gap in time between the creation session and the first Prelude. There will likely be some tailoring needed once you know the characters. But that's not a huge problem most of the time.
Character Creation for the Mechanics and the Meta
The Character Creation session should be used as a chance to have players become familiar with the system if they aren't already, and to discuss a few details of their characters to ensure they will work together and not have too much overlap.
You also have players discuss meta elements. Perhaps two players want to play rivals. They can discuss these details during this process, decide why they're going to be rivals.
Work up the full character, but I'd suggest telling players that no choices are final. Give them a chance to make changes once they better understand the mechanics and the setting.
During this part of the process, you needn't discuss more than the bare minimum of setting details. You know, just enough to make sure the characters will all fit within the premise. "You're all newly embraced kindred in the crazy world of high finance in the 1980s. Think American Psycho meets Vampire Diaries." Just enough to ensure the characters will work in your premise, and no more.
Prelude for the Setting and Story
Once you have the characters set, you can run individual preludes. This is the stage where you begin to introduce setting and story elements, and it can be run as free of mechanics as you and your players are comfortable with.
It need not be less interesting just because the characters are mortals. But making a story compelling does depend a lot on the GM. If you make the journey memorable, it will be awesome.
The last time I played Vampire, my GM did it this way. I built my Assamite, and then we roleplayed his journey from boy, to man, to trained assassin, right up to the scene where his mentor bites him on the neck and then hangs him up on a meathook. It was horrifying, and gut churning, but it was never dull. Along the way, my GM hinted at what it meant for the future.
You mentioned Initiations in Dogs in the Vineyard. As a GM, I've used this idea in preludes for other World of Darkness games (and other games) to help make them memorable. Players make characters, and then I ask them to ask a question we will answer during the prelude. This helps keep them engaged as they search for their answers.
This way will preserve nice balance between player agency and GM mystery. Players have freedom to create the characters they envision within the limits of the premise, but the GM doesn't reveal too many secrets too soon. I've played it, and run it, and it works well.
Best Answer
Blades in the Dark works with custom settings, as long as those settings match the assumptions of the system.
The Doskvol setting is presented in the book to give groups a clear starting point, but can be replaced with another setting with some work to replace the factions, major NPCs and regions of the city. This is quite frequently done; it's not a trivial amount of work, but nothing's stopping you.
It is, however, important to understand what details the mechanics hook into.
The interplay of the PC crew with NPC factions is mechanised by reputation and relationship scores, so it's important to make sure you have a range of groups for the PCs to aid, anger and generally get entangled with in the course of their scores. Similarly, the Entanglement and imprisonment mechanics assume there is a police force and incarceration system - if your custom setting removes those, you'll also need to change the mechanics that rest on them.
Also important is the set of Action ratings (skills available to PCs). The breadth of these is important - there are mechanical incentives to invest in a broad range of them, so in a setting where some of the Actions are less appropriate, just removing them will have game-balance repercussions.
This is particularly relevant to your thoughts because you say:
Two of the action ratings are Tinker, associated with building, repairing and manipulating technology (including things like locks and doorhinges), and Attune, which in the core setting is primarily associated with touching the Ghost Field.
One of the system's assumptions is that all the actions are available to all PCs - you don't have to be a trained medium to try and sense ghosts, but it will be difficult and stressful if this isn't a core part of your skillset. The inclusion of Attune on the Action list means the assumption that interaction with some sort of mystical or supernatural force is a possible approach for any PC to take in appropriate situations.
With that in mind, you're going to need to think about what to do with those two actions. Replacing the ghosts with some other kind of supernatural force is perfectly viable - Scum and Villainy, a space-opera hack of Blades, still uses Attune but has it associated with something much like the Force from Star Wars, and that's doable simply by explaining in what circumstances Attune can be used and what results it gets - but there needs to be something. Similarly, Tinker is a significantly weaker choice in a setting without complex technology, which has wider repercussions on the balance between the game's Attributes.
Elements like Crew types and playbook special abilities are less of a problem, as simply not taking a special ability that references ghosts doesn't have such broad consequences. Options get a bit narrower, and the Whisper might not be a viable choice since they only have a small number of non-ghost special ability options, but there's plenty of space left for people to work in.
Your custom setting is certainly viable but may require mechanical changes that wouldn't be required for one that stays closer to the supernatural and technological context of the original setting.