We need to agree on two new digits and some names for numbers.
If we look at the modern words for our numbers we can see that they have been evolving for many years and a certain amount of erosion has taken place.
Four tens and nine has become for-ty five
So our dozenal system should have this contraction factored in
ie. Four dozens and five becomes for-zy five
Thirteen becomes one-zy one *11
Next is the problem of ten and eleven
For ten I think a nod to the Romans is called for here and the amount 'ten' should be re-named 'dec' the symbol being a stylised 'd'.
Ok now for the eleven. Bit more tricky for the name, but surely the symbol has to be something like epsilon.
I think that keeping the stem of eleven will ease recognition so I'm proposing the German word for eleven which is elf.
Therefore the mouthful of 'one hundred and thirty-one' is reduced to *dec-zy elf.