DISCLAIMER: THIS REVIEW HAS SOME SPOILERS
Having finally finished Tatami Galaxy, It was a much more profound experience that I initially took it for. I can understand why people would consider this a cult classic. I have never written a full on review of an anime before so please bear with me and my eccentricity in compiling these various thoughts in my head together. :D
Similar to Christopher Nolan's films, the structuring of each episode is deliberately episodic, despite people might argue against. From an objective perspective, here's how it'll go:
With that in mind, I would say that barring episode 10 - 11, it has the opportunity to be viewed in whichever order up until then and you would still get the basic understanding of the plot regardless. Though what shines out about this series is that you can view it with a different lens, by focusing on the individual supporting characters. It is through the interconnections of Watashi's interactions with various others in various scenarios that brings a more in depth view of the overarching plot line being woven here. Each character has become an individual of their own in this world with facets/personas that we can only see a part of at any given time often blinded by whatever color tinted lens Watashi is perceiving the world through at that point.You'll notice that it is deliberately done in the episodes involving Keiko, Kanuki and Kaori below.

As you near the end of the series, you'll start to feel the significance of the op/ed in the meaning of both the lyrics and the overall theme that they chose for the series, the 4.5 tatami room. For most people, in this day and age, struggling with the monotony of reality, looking towards escapism hoping for a better possibility, evokes a pure human urge from the viewer. Throughout Watashi's journey in the 11 episode series, his tatami room has been the quintessential totem that ties all the roads of possibilities together, "never changing". We see that Watashi is able to traverse all of his various possibilities which spoke volumes to human nature as a whole.
When strangers meet, they often gravitate to what information their senses can provide for them initially to help inform them on how to interact. However, like subject matter and higher education, it takes time for people gain a better understanding of each other, through listening, communicating,etc. Though everyone is a human at the end of the day, no one person is the same as the other as differences in experiences and opportunities make up our identities as unique individuals.
Despite the various tatamis rooms interconnected with the room Watashi arrived in, there are subtle differences among the various possibilities:
In layman's terms, how anime fans create their 3x3 of anime/manga defining themselves as human beings is a good representation and analogy for how the tatami room showcase is portrayed.

Tatami Galaxy is heavily influenced by Mosaic-ism in which we are the sum of all that we admired from our peers. Having Watashi aim for a rose-colored university career with a black haired maiden is a fallacy in it of itself because to want it would be to reject all the other shades of color to his world thereby rejecting different colors that come into his life.
Like Master Higuchi has said:
"There is nothing rose-colored in this world. Everything is all a bunch of color mixed up."

Despite having past glories and trauma weigh on you, being the best you that you can be in this moment is the main focus for the present you.
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