I think the problem stems also in part from that while the 1900's and 1910's may have been called the 'oughts and 19-tens or 19-teens, those terms aren't extrem

I think the problem stems also in part from that while the 1900's and 1910's may have been called the 'oughts and 19-tens or 19-teens, those terms aren't extremely common today and "twenty-teens" also sounds strange. "twenty-tens" sounds to me a little bit like you're referring to the year 2010 in plural since the year is in recent memory. I will be very much surprised if "20's" does not come to refer to the 2020's; even more so if "30's" doesn't make it.