I might have been a bit too quick to reject the south-facing LEDs. I realized that in my experiments I didn’t mount the aluminum top plate, which of course covers the direct LED flares I was annoyed by. This means that south facing would work just fine.
I soldered on the full matrix and tested it mounted with the top plate and keycaps and it look great! In the video I’m using transparent switches which maximizes the brightness and spread of the illumination. When using non transparent switches I think the light would not blend together as much and the label on the keycap would not be as bright. I still think I’ll swap it around to north facing though just to make the labels of the keycaps illuminate just a bit more.
VIA
Additionally I enabled VIA configuration on the board and tried that. Not fully configured for it yet but it works and makes it very easy to change illumination modes. 
More derp
This is what prototypes are for, but I found another mistake. The alignment of the spacebar is wrong and does not match that of the top plate. It off by a mm which is enough to make the switch not fit. Quick fix, but very lucky that I found this!