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I still think doing a system using actual/stylized mayan glyphs or a similar system would be cool.
Mayan glyphs both acted as characters to form words and phrases, and they also often visually depicted what they refereed to. So the glyph for tree looks like a leaf, fire looks like flames, etc. Since they also were actually used as units of words and phrases, they are also designed to connect to each other.
So they could work as both individual, separated badges (which they actually resemble), as well as combing in multiple configurations, which could make for a puzzle.