So I tried this and it appeared to work:
Phase I:
- Created New Shared Parameter named Test_1
- Created Project Parameter
- New Generic Model Family
- Length Parameter Test_1
- loaded Family Into Project
- Both Project and Family were Test_1
Phase II:
- Manually Renamed Shared Parameter to Test_2
- Started New Project WITHOUT Test_1 in it
- Created Project Parameter with Test_2
- Loaded Family with Test_1 into Project
- Family Parameter name is now Test_2
- Closed Family
- Edited Family from Project
- Family Shared Parameter is Now Test_2
There are several steps here, but I think most of this could be easily automated. In fact, I have shared a post in the past that deal with loading, editing, saving and reloading families before that may be a place to start.
I know there are other packages that have Family Tools in them as well.