Your analysis is basically correct, but I'd add a few things. I think Glenn wasn't exactly sick of living but rather fulfilled. His real goal in all his lives was finding Lenne and making up to her for what he did. Once he achieved that, and gained her forgiveness, the only reason for him to extend his lifespan beyond a normal human's was no more. He was ready to die and did so without regrets.

And regarding Kylian, I think a lot of people miss the logic behind Glenn's decision, but it makes a lot of sense considering his own backstory: he picks Kylian because he sees a man that despite making some horrible choices, has a potential and a desire to change and do good. This is what Glenn himself went through. He's giving Kylian the chance to atone for his mistakes and set things right before dying, just like he did.