"But that has an established meaning, namely 1900-1909"

Not to anyone I have ever known. I have never before this post today heard anyone say that "the nineteen hundreds" means 1900-1909. It always refers to 1900-1999.

I've only ever heard of 1900-1909 referred to as "the aughts" ( https://en.wikipedia.org/wiki/Aughts ) - which, admittedly, always sounded weird to me, but I wasn't alive then.