No blendshapes for Actions; is there another way?

Would it be possible to play an expression in the fx layer during an action? How would I trigger it?

By using a sync parameter? You can add some or use the default ones that comes with the expression parameters.

Whenever your expression or emote plays, it alters a parameter in order for it to play that. That same parameter could be used to trigger another animation in a different layer assuming it’s a sync parameter.