Update 4: Player Choice pt II and More Writing.
Another update with writing progress and thoughts about feedback from the comments. Work on the game has really crawled to a halt as I've been studying for my exams for the past week. I finished the exams today and will probably have more updates as I work on writing over the weekend.
Narrative and Player Choice
I thought I would further update y'all on some specific decisions I made about the structure of the narrative.
1) The protagonist exists alone.
That is to say, there is no back and forth dialogue between the protagonist and another character. The high level plot is simply a 20 something college kid makes breakfast before his class. The reason for this specific design is for a few reasons. First, it simplifies the writing process tremendously. Writing another character well was simply out of the scope of what I wanted to accomplish. Secondly, I wanted to create a sense of intimacy. The game essentially exists within the thoughts and actions of a single person's mind and as such I wanted to delve deep into that aspect of the protagonist. Secondly, I wanted to limit the player's agency within the game. The player is not an active member of the plot. In this game I imagine the player more as a curious adventurer within the mind of the protagonist. Instead of influencing the protagonist, you were tasked with uncovering who the protagonist is through reading the thoughts of the protagonist. In a sense you are a passive observer who is given a situation and needs to parse out what is happening.
This also influences how certain scenes can be designed. For example in this scene that I showed earlier: 
The player here is presented with a choice. They can either click on "some papers" or "you close it".
Neither option affects the movement of the protagonist. (ie. clicking "you close it" does not close the door. The protagonist has already walked out of the room and closed it). The option does however lead into areas of the game that can provide greater context or more texture to certain ideas allowing the player to further uncover questions such as "who is the protagonist, why is his/her room messy, etc." It is ultimately up to the player however to be curious and uncover the world.
2) Regarding Choice and Player Agency
One of the comments above really helped me work through and sharpen my focus on this point. As I've written above, the player is separate from the protag. This can lead to some interesting narrative decisions. What if, for instance, the player wants to do something that would be against the protag's character? How is this addressed through the narrative? What kind of emotions can this bring about? How can this disconnect add depth to the story?
In my game I'm attempting to address this question by deliberately presenting the player with options that the protagonist would be against. For example in this scene: 
The option "Don't Eat" leads to a narrative path about the protagonist's childhood and how breakfast was one of the happy moments of family gathering. It is a narrative hook that I have included both to add detail about the protagonist but also to indue a sense of guilt to the player who decides to choose this. I'm not sure how effective this will be in practice, but we'll see! There are other ways in which I am exploring how including player choice can impact the relationship between the player and the protagonist.
Updates on Writing
Progress has been made! Though it's been slow. I'm about a third of the way through the middle. But I've written out a second ending! Yay! It feels like as I write, the more ambitious the project becomes. It's an enjoyable process but sometimes I have found myself losing sight of the scope and including things without considering them fully. It's also been a lot harder than I anticipated. Keeping track of what kinds of information the player knows given various permutations going through the game has been tough.
Interestingly enough I've been keeping up with most of my design goals. There is a lot more detail now in the game with various things that you can learn about or pathways you can explore. Also thinking about player choice and the puzzle of how to write around these game-specific situations is helping me create more interesting narratives I hope.
The Goal is to finish writing by Monday and start working on graphics during the week! Let's see how this goes.
Random Thoughts
Being in this process of development has also been really fascinating. All the people I've interacted with have heard by now that I'm working on something and I find myself frequently thinking about other projects: just everyday experiences that I'll go through and think: oh that would make a fun/interesting/weird game. There's this surprising energy and excitement that I have to the development process in general. It's been really fun to play with all these ideas and thoughts and theories that I've read on development sites.
Honestly, I don't think I've enjoyed doing anything this much in a long time.