Also, that map seems incomplete by at least a 3rd. The connection between it and Shinjuku-3-chome station is missing (the hallways just arbitrarily stop on that map) and the tunnels from there to the south entrance of Shinjuku station are missing as well as 3 more train platforms. I suppose you could argue that's a different station which is fine, but the fact that tunnels don't end where they appear to on this map is misleading.
https://en.wikipedia.org/wiki/List_of_busiest_railway_statio...
But you could do it in Quake.
Instead, familiarize yourself with the general layout. There's no need to memorize the entire map, only the portion you will be using. Inside the station there are plenty of signs overhead and even on the floor to help navigate.
Also, I am curious of the justification. Why would anyone place signs that "... are incredibly confusing and often will all point to each other from every direction."
Signs are mostly useful for people who are new to a place, if you need a significant amount of time to familiarize yourself then they are useless.
There are multiple ways to get to various lines' platforms. This is not signs pointing to each other, this is signs in different places pointing to the same destination.
I live in Tokyo and while I do not go through Shinjuku often as I mostly live and work on the east side, I have no issue using the signs to find the platforms and exits I am looking for.
If you pay attention to what the signs have written on them, they will take you where you are trying to go.