'Immortal'.
It was simply too vast a concept for Jack to really appreciate. Jack wasn't a hypocrite — not staying dead was damn useful. But as time wore on, he took more and more comfort in the fact that he was aging. He didn't let the fact that the aging didn't have a particularly linear relationship to the time he lived bother him. Who knew what the rules were? He was aging, no matter how slowly, and old age wasn't a death he had ever tried before.
Millennia passed, and Earth grew up. When they gently suggested he was getting a little old for world-saving, he retired gratefully to a little pioneer settlement that reminded him of his childhood home. He played 'great-uncle Jax' to generations of youngsters without once ever dying. Then disaster struck. Old and out-of-touch and useless, the best he could do was shelter two children from the blasts and then hide them from the raiders. He lost count of how many times he died over the next year, as if to make up for the selfish centuries he had lived before. He noticed himself getting fitter and stronger, but it wasn't until he was back in civilisation with razors and mirrors that he was forced to acknowledge the truth — his aging had reversed.
Millennia more. Jack fine-tuned his control of his physical age, changing it for variety, practicality and to throw the inevitable pursuers off his trail. Intermittently his mood drove him to inventive suicide attempts. Some were more painful than others. Cutting of his head, for example, was worse than cremation, because with his head cut off he could feel his body reconstructing. With disintegration, by the time his brain kicked back into gear the rest of his body was already intact.
He saved his brightest idea for last — create a temporal paradox and let the reapers take him. He did his research meticulously, and settled on an uninhabited asteroid in a planetless star system for what would hopefully be his final self-cleaning con. He established a base, read a book, and generally loafed around for a day. Then he went back in time to establish a base and waited for himself. When he arrived, he had the bizarre sensation of being mentally split. He was both future-Jack and past-Jack. He walked over and hugged himself, and his fears were confirmed. No reapers. He didn't say anything — talking to himself felt a little like playing with sockpuppets — but he didn't have any objection to masturbation.
He had thought he was prepared to consign himself to the super black hole as the end of the universe, but it turned out he wasn't. He didn't know if he'd retain consciousness in the agony of being torn apart, but the thought of eternal pain awakened long forgotten fears. Typical human after all — afraid of going to hell after death. He no longer needed his vortex manipulator for short time hops, and it didn't take much practice until he was managing longer and longer periods. He went all the way back, back to before the dark times. Then, with deliberation, he navigated to the Issop galaxy. Those old jokes about the Face of Boe —maybe they weren't jokes after all.
When he met the Face of Boe, his first reaction was that this must be, this had to be, an older version of himself. Even if he couldn't see why he'd ever decide to look like that. But he couldn't fool himself for long. The mind was strong and so was his, and they couldn't help but gain impressions of each other. The Face of Boe was young, so very young. Powerful and scared in that power and desperate for an older mind to guide him. Jack wasn't the kind of person who could refuse, and he wasn't the kind of person to mourn lost hope for long. It wasn't until very much later that he started to wonder whether he himself had taught the control of aging that would result in the Face of Boe living for most of the life-span of the universe, alone and lonely.
He decided to make one last attempt to fix himself, before consigning himself to a black hole. He would return to the height of the Time Lord reign as a Time Lord, and research the vortex and himself. The strain of picking the time lock was not inconsiderable, and his alteration of physical form to that of a Time Lord foetus was even worse. As a result, it took him absurdly, criminally, long to realise that he had vastly overshot his mark and wasn't named after Rassilon.
After fearing it for twice the lifetime of the universe, the experience of a black hole caused him to laugh himself into hysterics. The very briefest perception of pain, and then coming back to life at the beginning of the universe. Not even the beginning of a new universe, which would at least have given him hope of different types of death. The timelines were a shimmering sea of possibilities, but instantly recognisable for all that. The experience with being a Time Lord was the only thing that kept him sane — he might have to live through it all again, but he wouldn't have to remember it. He could become the burgeoning life and live it without baggage. At least until he died.
After living as Ianto Jones, he cried. After living as the Face of Boe, he laughed. By the time he lived as the Doctor, he merely paused in fond remembrance. Some sentience took more control before he could live as them — sun based life forms, physical manifestations of metaphysical concepts, and so on. Others he never lost his awareness to become. Reapers, for example, were a conscious manifestation of his will, returning himself to himself whenever the rules were broken too badly to repair.
He became the last of the inanimate objects more from a sense of completeness than from any need for uniqueness. When it was done, he opened his mind to himself. He became all things, in all places, at all times.
Playing endless games of solitaire.