Brother Joe,
I appreciate your post's and at the same time I would like to suggest that a New Testament Church which is "a body of Christ," be referred to as just that, without having to describe it as "local" since it is implied in what it stands for and the redundancy only creates confusion as if there really is a "Universal Church or Body". For instance, what if I referenced a verse of Scripture like this:
(Matthew 3:11, King James Bible)
“11 I indeed baptize you with [WET] water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with [HOT] fire:”
The Scriptures are clear on what makes an assembly, "called together in one place," whether it is a Jewish assembly called a synagogue, a Roman assembly called a church or Jesus's assemblies called His Church.
Hope my two cents helped!
Brother Michael
(1Corinthians 11:20, King James Bible)
“20 When ye come together therefore into one place,..."