As you probably know, the UK (and much of our Empire) used to have Pounds (£, L), shillings (s, /) and pence (d). I'm not going to get into that system in this post but to say the following things.
We have 12 inches to a foot, and there is no issue. For smaller units, we subdivide the inch.
In pre-decimal times (y'know, that short time frame from around the 700s anno domini to 1971), there were twelve pennies to a shilling. The penny itself was divided into ha'pennies / halfpennies, farthings (fourths of a penny), and at many times, third-farthings (i.e. twelfths of a penny).
The shilling, from 1816 to 1971, was 1/5 of an avoirdupois sterling (0.925) ounce of silver in weight, so almost 1/6 oz troy (about 1/5.6, actually), but "originally"* would have been equal to 6/10 of an ounce.
So.... I haven't seen it put forward much, but I don't see why the SHILLING can't be the dozenal currency, itself being equal to (say) 1/6 oz silver; twelve pennies would make up the shilling, and twelve third-farthings to a penny; higher multiples would be 3, 6, 12, and so on, so the 6 shilling would handily be one ounce of silver.
Just a thought.
Alternatively, the "dozenal currency" could simply be the ounce (troy), as there are twelve troy ounces to a pound, and the ounce itself could be divided into 24 (i.e. 2 x 12) scruples...
That's just another thought.
*It's a long story. I'm simplifying.
In fact, this system was devised by Charlemagne and first used in France: «The livre was established by Charlemagne as a unit of account equal to one pound of silver. It was subdivided into 20 sous (also sols), each of 12 deniers.»
livres, sous, deniers: £ s d