Nice to see your goals laid out. All I can say is please don’t get rid of the goofy stuff; it makes the game colourful, even if you are going for post-apocalypse.
I’d say that the Growth and Survival stages are in full effect right now, but the latter two I haven’t felt yet. Influence is a bit vaguely defined and seems more akin to Survival than its own stage the way you described it. With the term ‘influence’ I was expecting the beginnings of a community or following of NPCs. More than merely surviving, you begin to carve out your place in the new world; whether that be with the helping hand of a friendly band or the bloody berth of scorched earth. (I like alliteration). Somewhere between “I know how to survive” and “I am the mayor of Megaton”.
Trancendance seems pretty accurate though; established bases, advanced science, all good fun. The term is interesting too; I’d imagine this as a whole new tier of personal enhancement. Either through your loyal followers, advanced tech, formidable arsenal or nightmarish form, turning you into some huge level of legendary badass. It’d be cool to cap the endgame with fighting the big bads of the apocalypse, like the Blob or Fungal Hordes. Boss-style encounters once you’re kitted out enough.
Also I may be personally biased towards this, but being able to mutate your way to horrific perfection is always a fun prospect.