One of the sources of the alternation between stop and nasal codas—the ‘陽入對轉’ of traditional Chinese phonology—is assimilation of a final stop to the nasal initial of the following word. An example is the expression zhēng yuè 正月 ‘first month of the lunar year’. The earliest secure occurrence of 正月 I am aware of, referring to the first month, is in the Luan Shu Fou 䜌書缶, a Zhou bronze inscription:「正月季春元日」’on the first day of the first month’. Palaeographers would probably know earlier ones. The character 正 normally writes *teŋ-s > tsyeng > zhèng ‘correct (adj., v.)’. How did it become used to express the meaning ‘first’ ?
There is in Western Sino-Tibetan (a.k.a. ‘Tibeto-Burman’) a root for ‘one’ which the STEDT website reconstructs as
#2726 PTB *tyak ⪤ *g-t(y)ik ONE (provisional).
The corresponding Chinese root reconstructs as *tek ‘single, only, only one’. It includes these words:
隻 *tek > tsyek > zhī ‘single’ 1260c, 適 *s-tek > syek > shì ‘only’ 0877s, 啻 *s-tek-s > syeH > shì ‘only’ 0877k.
Root *tek and the root in 正 *teŋ-s differ only in the nasality of the coda. This suggests 正 writes 隻 *tek ‘1’ in a context where its ending had become nasalized. The onset of the following word: 月 *[ŋ]ʷat is likely where nasality comes from. 正月 was an appropriate way of putting *teŋ-ŋʷat < *tek-ŋʷat into readable form.
Reference
Liu Shiru. 1965. Weijin Nanbei chao liangci yanjiu (Studies on Classifiers in Wei-Jin and Nan-Bei dynasties). Beijing: Zhonghua.
In Baxter and Sagart (2014), 正 was previously reconstructed *C.teŋ based on the evidence from Vietnamese and Min. Under this new proposal, would this mean there’s some prefix *C-?
I also note that one traditional account for the irregular reading for 正 suggests that it is due to taboo avoidance of homophonous 政 (the name of Qin Shi Huang) (史記正義: 始皇以正月旦生於趙因為政後以始皇諱故音征). Am I right in thinking that this new proposal would conflict with this account?
You are right that the new explanation clashes with the taboo avoidance account. As mentioned in the post, the expression 正月 occurs in the Luan Shu Fou 䜌書缶, an early Zhou bronze inscription, well before Qin Shi Huang. As to the prefix question, when 隻 *tek became *teŋ under the influence of ŋ- at the onset of 月, this made 正 *C.teŋ an expedient way of putting it into script, regardless of whether the *C. was a prefix or not. The notation *C.teŋ means we do not know whether C. was part of the root or a prefix. That 正 *C.teŋ was used to write *teŋ < tek-ŋ has no bearing on the nature of *C.