Words for numbers in a language with bijective numeration

Bijective base-k numeration (or k-adic numeration) is a system of writing numerals such that the digits are 1 through k. Thus counting in bijective base-12 (such as my conlang Atili has) works as follows, using X, E, and T for ten, eleven, and twelve, respectively:

 1,  2,  3,  4,  5,  6,  7,  8,  9,  X,  E,  T,
11, 12, 13, 14, 15, 16, 17, 18, 19, 1X, 1E, 1T,
21, 22, 23, 24, 25, 26, 27, 28, 29, 2X, 2E, 2T,
...

What are reasonable ways to assign names to these numbers, specifically combining tens? Obviously, I could just name the numbers the way English does and just have the names for numbers not line up with how they are written (so "a dozen" would be T, but "a dozen and one" 11), but are there other solutions for naming that better align with the way that numbers are written?