Predicates

1a. I had an army, not just any old army either. No, I had ...

1b. I had an army. Not just any old army either. No, I had...



2a. There is no example of its use where I come from, not one instance of it in any authoritative sources.
2b. There is no example of its use where I come from. Not one instance of it in any authoritative sources.



3a.We need to be the best we can be, not hampered by...

3b. We need to be the best we can be. Not hampered by...

1) Are we meant to treat the emboldened words in both pairs of sentences as second predicates or new independent clauses with the subject and verb omitted (I had & There is & We need to be)?

Thank you