I would like to say my procrastination was because I knew on some level of the previously mentioned problem

I would also like a moon base. Totally didn’t realize it until I actually cut wire. No use crying over spoiled milk.
Using 12 output pins (beyond the lack of 12 pwm pins) would be the easiest solution. Since I’m wanting to go pwm rather than persistence of vision, I’m limited to something like six out and no using the D in LED.
I think, assuming no desire to massively change the concept, I might just go all chaos on the wiring. If there were more input and output wire combinations than I really needed I could have pseudo randomization. Like six “rows” going to four sinks might work. Of course, this would start to diminish my extensibility rather fast. I might have to start doing some charts.