The thing is, I don’t think you want to move the player character from time-room to time-room. Unless fancy time travel shenanigans are involved, if I pick up a wrench in 2019 before I start remembering 2007, I shouldn’t be carrying the wrench back in 2007.
So the thing to do is instead to have a copy of the player character in each time room. We can associate each version of the character with the room where it belongs, like this:
A room has a person called contemporary.
December is a room.
Decemberself is a person in December. The contemporary of December is Decemberself. The player is Decemberself.
January is a room.
Januaryself is a person in January. The contemporary of January is Januaryself.
April is a room.
Aprilself is a person in April. The contemporary of April is Aprilself.
So now each “self” is its own individual, who can have its own inventory, a unique description (which will print when you EXAMINE ME), and any number of other properties that don’t extend to the other selves.
It’s (probably) important to declare immediately that the player is the contemporary of the default timeframe, so that you can return to being that person when necessary.
The remembering action then needs to understand the name of a room, figure out who the contemporary of that room is, and pass control of the player to that person. (Also, we don’t want to re-become our current self if we happen to remember the current moment. I think.)
Remembering is an action applying to one thing. Understand "remember [any room]" as remembering.
Instead of remembering:
say "You remember it like it was yesterday…[paragraph break]";
now the player is the contemporary of the noun;
if the contemporary of the noun is the player:
say "You are remembering that right now." instead.
True blue codemasters will say that the “Before remembering” rule should be “Check remembering” instead, but I couldn’t make it work as a check rule. So, tell me what I’m doing wrong, true blue codemasters!
(I think you could also/instead say that a region has “a person called contemporary,” and have the remember action turn you into the contemporary of that region. That way, you could have multiple rooms within a timeframe for the player to explore, and whenever you remembered that timeframe, you’d show up wherever that self left off.)