His first priority is making sure he doesn't die while he's busy sorting everything else out.
He lays both hands flat on the floor of the monument and closes his eyes and explores its magic with his Sense. There's the part for sustaining his life - can he pull out a copy with rilte—? No, not quite, but he can spend a few hours studying its structure and then very carefully build himself a temporary version. Okay, there's his survival taken care of for the next few months at least. Now what?
Now he designs himself the perfect kind of immortality, that's what. The ability to die is a luxury he can no longer afford.
He needs to be not only immortal but also invincible, or at least proof against anything Reihar Nirue might try to do to him. But he also needs to avoid closing off potential avenues for improvement. He should be able to modify himself, but he should be the only thing that can - except that if he takes that principle too literally, he'll end up with all his external senses cut off because outside information would cause changes in his mind, or something similarly stupid. Careful, careful, careful.
A few hours' practice with rilte and ileyi gets him to the point where he can reliably supply himself with pen and paper. He starts making notes. The monument didn't do it, but someone else could - he needs to be immune to magical mind control, and he should probably also make his mind impenetrable to outside inspection - but for cases like communicating with the monument, he should probably be able to share his thoughts deliberately...
And on and on, through hundreds of different ideas for what should and should not be allowed to happen to him. Not only should he not be able to die, he should also not be able to become trapped. That's a hard problem, though, and probably relates to interworld transportation; he'll save it for after he has his basic immortality worked out. He should be able to eat and drink and sleep and breathe and so on, but not require any of those things in order to remain comfortable and functional. He should not be susceptible to aging, or to illness or injury or miscellaneous deterioration.
It may be tempting to explore potential improvements - make himself think faster, that sort of thing - but he should focus on the necessities of basic immortality first, and experiment with more daring self-modifications afterward, slowly. He has time; he does not have a spare Korovai if something happens to the first one.
...he could create a spare Korovai.
But that would be a significant undertaking, and could itself potentially go wrong in damaging ways, and he still needs to get his basic immortality out of the way before he starts in on other improvements.
It comes as a considerable surprise to him when he looks up from his notes and realizes that he is hungry. He's been distantly aware of the passage of time, but clearly not paying it enough attention if three months could go by while he was distracted.
Does he have everything he needs?
Not quite. He spends a few minutes reapplying the temporary fix, and then, no longer distracted by hunger, dives back into his notes. Three months later when the ward wears off again, he has his basic immortality designed and ready to implement.
Kiina to strongly reinforce his tendency to be himself. Beshenn and soryo for endurance and stability. Ileyi for inexhaustible energy. Poai to handle the biological side. Rilte for small improvements to how it all works. Kiina and beshenn again, and a touch of tsaer, to emphatically ensure that he is the only person who will ever be able to alter any of this.
There. Done.
Now to work on getting home.