You are correct that there is not a built-in structure for this currently as there is not a symbol equivalent for just the animations. Symbols require elements to all be the same.
However, there is a new project that allows for symbol overrides that could probably be employed here. See:
I imagine you could just override the innerHTML property, and potentially apply this to multiple elements like the bouncing text as well as the shadow.
To offset the animation timing, I'd probably just change the start time of the symbol action on its parent timeline.