How do you prevent overlapping audio for layers when layer text must remain on screen?

You could add a trigger to the base buttons that toggles a T/F variable. Whether it's True or False doesn't matter. But you could use "pause audio when variable changes" in triggers on the layers.

Or here are a couple of methods that ensure someone listens to all the audio:

• On each layer, add an object that covers the buttons on the base. For example, use a semi-transparent shape, or anything that makes it visually obvious that the user can't click those buttons. Give those shapes exit animations, so they'll disappear when the timeline ends. This trick will allow users to click another button only after the audio plays. 

or

• Add triggers to each base button that disable the other buttons. Then add triggers to each layer that enable all the base buttons when the timeline ends.