Let me see if I can help some here. After reading your description I felt beside "Shared Parameters" you will need to look into "Shared Families" in what you are trying to achieve. If I am making an understanding that you have nested families with same parameter names with different data that now you want to somehow wire back to the parent object. If wiring back to the parent object is not important then perhaps your naming for parameter names would be rather much simple.
Let me consider an example.
Consider if human body was a Revit family. The full body is a family with a parameter name "Name". Now each body has two hands. Right and Left. And each hands have 5 fingers. Thumb, pointing finger, middle finger, ring finger and the little finger. All of these different objects will have the same parameter "Name" to identify what they are. Essentially their names is what we are tracking using the parameter name "Name."
By doing this we created an identification system for each part. If I were to refer a Right hand thumb like this,
Rabi.Right Hand.Thumb
Ciara.Right Hand.Thumb
it would simply make them unique because one thumb belongs to Rabi while the other one belongs to you. Considering the dot represents the heirarchy of nesting, you could design this family with basically one parameter called "Name".
Now if you were to control all of these data from one parent family, then you will need to name each and every part you want to control uniquely at the parent level itself. Let me define it with my example above.
Say I want to see the data "Thumb" at parent level family. I would probably have to create parameter names like this.
Human.LeftHand.Finger1 = "Thumb"
Human.RightHand.Finger1 = "Thumb"
each item above would be a parameter name. These parameters then will be wired back into all nested levels such that they are uniquely represented at the parent level itself. This may make it super complicated. What possibly could be solved by "Name" parameter all of a sudden becomes so daunting.
I recommend you look into Shared Families. It would help you design your workflow by making it possible to uniquely define each part as its own identity while still associating them with the parent family. A complex data system can be then addressed with simple parameter names.
Now where "Shared Parameters" are unique is that they will help you create a unique data field that you could utilize in all of your nested families. Project Parameters have their own ID's and they are not the same thing between two families. Revit utilizes GUID's for identifying the data field and not the parameter names we pick. Thus you would need to use the Shared Parmerters so they are the same data field that you need to define in each nested families.
You could than create a schedule with all shared families and filter out what you don't need thus having access to all the nested level information you wanted to track.
I am sure you have lots of questions. Please feel free to elaborate and we shall try to explain them. Please let me know if this helps.