Not sure if is the best method or if you already did it but, try parenting the breasts components (control_01) to spine_C0_eff instead of spine_C0_root.
This way both breasts controls should follow chest movement, either using IK or FK.
And to make the joints scale at same rate of spine when stretching/squashing, for control_01 component on Joint Settings, do the Parent Joint Index be one index below the number of divisions you are using on spine_C0_root component (i.e. if you have 5 divisions, control_01 index should be 4).
In the image attached I built one side with the default settings on control_01 and the other I changed like described.
I hope it helps you.
Sorry, reading it again, maybe I misunderstood what you said
If possible, send a screenshot of the result you are getting and mark what is not behaving properly.