Forbidden Memories?

Warning: I’ll be discussing spoilers for Ambition: Light Fingers here.

I’ve just ascended to the roof of the Neath, and it mentions something particularly interesting: I am currently up in the false-sky, and everything I do in London at current is but a memory. I can freely travel between there and here, but anything I accomplish in London will have been accomplished in London before I took off. This leads to a rather…interesting turn of events where I could potentially pick one of the big endings of the game, such as going North through a certain door…while having that be but a memory. As such I’m curious, what exactly happens if you were to pick one of the big outs that end your character whilst up here? Had they even thought of such a thing?

Treachery of Clocks splits your life into multiple concurrent timelines, which are combined into a single being that is you.
Mechanically, you’ll still be finished.