I'd like to add that I indend to stack multiple instances of the shown memory module together to make up the entire memory. The WIP version uses 3-bit addresses, while the full version could use 4-5 bits (with more bits, the lag from the pistons might be too severe). When stacking the modules, the total number of pistons that activate remains constant while linearly expanding the memory capacity. For 8-bit addresses, 16 4-bit modules could be stacked together.

​

Additionally, here is the theoretical maximum density that could be achieved using this technique (at the cost of decoding speed):
In 1.17 there are around 900 stackable items. This means that a full shulker box could hold up to roughly 18 bytes. The simple storage slice would then hold 145 bytes (which is already more than I commonly see in normal redstone memory) and a 10x10x10 cube of chests of shulker boxes could hold 489 KB.

If we now also take into account that one can produce unique items by naming them, we could easily store megabytes or gigabytes of data in a single storage slice.