After thinking about it I realized that the system I'm using doesn't have zero structure, but it has less than, say, multiplication tables.

I use the phonetic two digit Person-Action-Object system. So 23 for example corresponds to "Nemo nomming (a) gnome." (n=2 and m=3). 48 is "Raph raving (at a) ref." (r=4, f/v=8). 56 is "Luigi leashing a leach." (5=l, 6=sh/j/ch). This allows you to chunk 234856 as the vivid image "Nemo raving at a leach."

I'm still not quick enough with the system to say whether it's really useful. Part of the purpose of the exercise is to force myself to memorize something difficult just for the sake of getting a sense of what it is to memorize something, since I've avoided that activity for my entire life.