This answer relies on the assumption that your epic character has access to the Epic Level Handbook and is capable of using seeds to develop spells.
The Seed:Life spell, among other things, can
can cast a spell
developed with a special version of the life seed that gives
actual life to normally inanimate objects. You can give inanimate
plants and animals a soul, personality, and humanlike sentience.
The newly living object, intelligent animal, or sentient
plant is friendly toward you. An object or plant has characteristics
as if it were an animated object (see the Monster
Manual), except that its Intelligence, Wisdom, and Charisma
scores are all 3d6.
From what I can tell of the Living Vault, it can tell if a creature is physically its master, but it does not discern between souls- none of its abilities allow it to determine that the master is a victim of magic jar, for example. If you don't want to fight the Red Wizard, your best bet is to animate the body with a different soul, and for all my searching this is the only thing that will bring a dead body to true life. At that point, your archmage can possess the body, or can choose not to bother, as the newly ensouled body is friendly toward you.
An alternative is to use the body to create an intelligent undead creature- from the magic jar spell:
Only sentient undead creatures have, or are, souls.
From create undead (it applies to create greater undead as well):
The spell must be cast on a dead body, and the DM may
assign specific requirements for various types of undead.
Nowhere does it say the corpse must have ever been alive, or had a soul. I'd recommend a vampire, as (from the vampire description):
A vampire uses all the base creature’s statistics and special abilities except as noted here.
A sufficiently generous DM could allow that this means the vampire would retain the original's spellcasting ability. Even if they don't, vampires are intelligent enough to learn how to cast- hopefully you're in no rush.
The creature will have a different type than the original, however, which could prove problematic... especially if the undead creature alters your new body in some way. Of course, depending on how you define a never-alive corpse, the seed above may also spell trouble; if you treat the corpse as an object, the newly friendly fellow with identical DNA to your Red Wizard would technically be an animated object. Ultimately, it might be better to try and fool the Red Wizard into a situation where you can use magic jar or similar on him.