How to create a colored strip following the top edge of irregular shapes?

I'm designing a board game in Illustrator with uniquely shaped spaces (see attached images). I need to add a colored strip that precisely follows the top edge of each game space.

This is how I want one space to look, with a colored section at the top portion.

This is my overall board game layout for context.

Is there an efficient way to create these strips that will automatically (or at least efficiently manualy) follow the contours of the top edges, considering each space has a unique shape?

Thanks for any suggestions!