They are in fact really, really preliminary!
...Altarrin has a pocket hidden in the Void. (Based on Carissa's knowledge of how the Void works, this should not really be possible.) His soul is tethered to it - it's sort of arguably blood-magic, but using his own life-force. Since the pocket is in the Void, and there is no extant mage-tradition that teaches mages to project their minds to the Void - in fact, he suspects he invented it or taught it to himself in his first lifetime - it's extremely difficult to trace, and the gods haven't succeeded at it yet.
There's a bloodline spell that links to all of his male descendants. (This wasn't incredibly a deliberate choice because he disliked the thought of being a woman, it was just magically much easier for some reason - he thinks he might have once very confusingly ended up in a female-appearing body but it was during a period where he really doesn't have good records and he didn't survive that long.) When his soul is in the pocket, a ward-type spell watches for the trigger event, which is a mage-gifted male descendent casting a fire spell for the first time, and then - zoom.
He doesn't have to kill them, necessarily, he shared a few times, but it...distorted him, and he didn't like it, and also he wakes up in the body disoriented and usually evicts its previous inhabitant on sheer reflex. He doesn't like the cost but this is the method that survived the Cataclysm, his first few attempts to replicate methods that did not survive the Cataclysm but should have worked were disrupted, and he eventually decided he would rather not keep giving the gods more information on this area of magic.
- he also can't replicate it now. He's pretty sure gods can intervene in the Void, if they know to look. But Carissa has some tools the gods are still mostly unaware of.
Other ideas: immortal artifacts. Someone's a sword. That particular case involved a divine intervention as well but he thinks you wouldn't have to have that. Multiple downsides, though – limited cognition, the sword seems less than fully sentient unless piggybacking on the mind of a Gifted bearer. Upside: doesn't kill anyone.
Inspired by that: sword that partially hosts your soul while you sneak in and 'reincarnate' into a fetus just before the usual time in gestation when souls attach. Downside is occasional long periods of reduced capacity and greater vulnerability. Upside: doesn't kill anyone unless you count a counterfactual baby whose soul would've landed there instead, but Altarrin doesn't.
Artifact that hosts a soul temporarily while you transfer it to a clone-body prepared in advance with a particular kind of bodyshaping magic. Altarrin created a species before the mage wars, and Urtho created a sentient species (gryphons), and it should be possible to create a one-off body that could hold an intelligent mind and attached soul and just...doesn't, yet. He has never gotten that far on attempting it, though, it's a high-resources project. He's curious if Carissa's Polymorph-type spells could cheat the difficulty entirely.
There are a few other more vaguely sketched out ideas - adapting the technique that gives summoned elementals construct bodies (but how to make it permanent?) - consensual agreements with carefully selected people to start bearing your immortal soul-artifact at a young age, grow into the 'other half' of your mind (downside: wow that sounds more lossy in terms of values and sense-of-self than Altarrin is even close to willing to tolerate, but it's definitely a continued existence...)