Very provisionally, I think you may have hit on a general principle there. If the structure of a word depends on the sizes of its components, you have to be able to count that. And to count, you need something like a stack - some extra component in any event.
How does that sound? (Will get back later on details. Right now this quiet little screen is competing with a vacuum machine, a conversation, and a washing machine, for my attention, and my concentration ain't so good).