While I agree about your choice of nomenclature, that it appeals to what authority used to be (now academia is bent on "affecting change" and "making the world a better place" in a certain self-loathing and destructive way, it seems; thereby the academy is corrupt, cf. University of Missouri lunacy), that it is steeped in our Roman western heritage, that it is not connected to decimal concepts, I am not sure it makes an impact UNLESS people actually use the word. The word "uncial", as pronounced at least here in the Midwest (UHN-see-ull) reminds me of onions. Because I am fluent in Italian by having learned it at one dozen nine years old, it reminds me of "unghi" or fingernails. It also reminds me of uncles, and by uncles, ankles.
We get an ounce and an inch from this word; perhaps you mentioned this before.
You would have us call "dozenal" "uncial"? The Uncial Bulletin. The Uncial Society. Uncial multiplication.
One advantage of "dozenal" is that people immediately understand the word or can get an idea of it from the first two syllables. "Duodecimal" unfortunately would evoke "Dewey decimal" and many took it to signify having to do with American library book filing systems. If I suggested Johnny use uncial arithmetic, it would be clear as mud. Of course, if our new usage would prove popular, like a new Camila Cabello song nah nah nah, then maybe it would be snappy and find traction.
I like uncial because it is more concise and does connect to the historic, decimal-free usage. Just not sure what you're looking for people to do. Changing what we call things has consequences. For instance, some time in the late 70s or early 80s, the Duodecimal Society of America, having been established in the thirties with that name, changed it with the State of New York to be "the Dozenal Society of America". Government is the least efficient way of doing things and somehow the State of New York was remiss, or the federal government nanny state was clueless, but that fact was lost upon our betters. Our then-president changed it again to "the Dozenal Society of America" in a formal government document more recently, within the past dozen years, and that is the document we cited when recently moving our account from one inept too-big-to-fail government bailout bank to another. It was a hassle and I am not sure we're free of it. In my view I am not sure what was wrong with keeping the original name, at least in this instance, and were it the Uncial Society of America I would feel the same. Things acquire names and then go by them; they are handles, like it or not, that people recognize at least somewhat, and if we change them even for good reasons (Bombay, Mumbai) sure it takes time getting used to it, even when Peking became Beijing, but how many people live in those cities? And how many people deal in uncials? Could people live and die a hearty good live of six dozen nine years and never once hear about uncials or deal with them? If so, it might be difficult to unseat a stubborn mal-usage once established.
But if you want, I'll personally call it uncial and we'll see where we go with it.