Reconstruction of Old Chinese "少"
Baxter–Sagart's (2014:135) view on *s.t-:

Preinitial *s- had a range of effects on unaspirated stops and affricates . . . Old Chinese *s.t-, but not *s.tʕ-, evolves to MC sy- (plausibly [ɕ]), presumably through an intermediate stage [stɕ] that simplified to the Middle Chinese palatal fricative sy- under the influence of pre-initial *s: *s.t- &gt; *stɕ- &gt; *ɕ- = sy-.

For 少, B–S's MC reconstruction is syewX. The consensus of MC is ɕiᴇuX. This is supported by the fanqie 書沼切 of the third division in Guangyun. All MC reconstructors concur the 書-initial is /ɕ/.

I believe B–S is aware of the conflict between the above theory and the presence of the 妙-type phono-semantic compounds. In fact, B–S applied the square brackets (which indicates uncertain identity, not lack of evidence, in which case parentheses would be used) to not only *s.t for 少, but also *m for the 妙-type phono-semantic compounds:

眇/杪/渺 *[m]ewʔ
妙 *[m]ew(ʔ)-s


Reconstruction evidence from the Chinese script is important but needs to be used with caution (Baxter–Sagart, 2014:26):

As with rhymes, in using evidence from the script to reconstruct Old Chinese, it is important to take into account not only which words were written with the same phonetic element, but also which words were not written with the same phonetic element. Traditional Chinese philologists noticed cases where initial consonants that were very different in later pronunciation were apparently treated as interchangeable in the early script.

The example 喻四古歸定 was immediately given where initials y- and d- in MC were often interchanged in OC:

弋 yì &lt; yik ‘shoot arrow with string attached’ is phonetic in
代 dài &lt; dojH ‘replace’


余 yú &lt; yo ‘I’ is phonetic in
涂 tú &lt; du ‘path’




Edit

In constructing OC for 少, Zhengzhang (2003:154) caters both the agreement with MC sy- and phono-semantic diversity.

*hCj- 則生成書母字，如「勢」hŋjeds、「恕」 hnjas、「手」hnjɯw' (「手」與「杻」為同族詞，跟兄弟語「手指」泰文 niu'、緬文 hnjoɯh、基諾語 n̥u 同源)。「少」可諧「秒杪眇渺妙」應是 *hmhjew'，這樣才能與「鈔訬吵」 *smhreew 相諧，並跟「小」 *smew' 轉注（小少與「秒眇」等同根，但與「沙」只是異源同形）。


As for *hCj- (C: consonant), they make characters of the 書-initial (MC sy-), such as 勢 ('potential', shì, OC *hŋjeds), 恕 ('to forgive', shù, OC *hnjas), and 手 ('hand', shǒu, OC *hnjɯw'). 手 and 杻 ('ancient instruments of torture', chǒu) are family characters, and is etymologically the same as 'finger' in Thai (niu'), Burmese (hnjoɯh), and Jino (n̥u). 少 concurs with 秒杪眇渺妙 and should be reconstructed as *hmhjew'. This is also to reflect *smhreew in 鈔訬吵 and to be derived cognates with 小 (*smew'). Note 小/少 and the 秒/眇-type phonosemantograms are of the same origin, but not with 沙.


Zhengzhang (2003:141) also considers the preinitial *s- to usually precede nasal consonants (which is not what B–S thinks, see obstruents in point 1.):

戌 *smid, 烕 *hmed, 滅 *med
小 *smewʔ, 少 *hmjewʔ, 渺/秒 mewʔ
需 *snjo, 儒/襦/孺/濡 *njo

Moreover, unlike B–S, Zhengzhang does not attribute any morphological function to the preinitial. It merely serves to apparently explain phono-semantic compounds and phonetic loans.

In defence of B–S's OC construction: what is different in B–S than previous reconstructions is that it is heavily inspired by Vietic, Hmong-Mien, and Kra-Dai because they received early loan words from Chinese. I looked up Hán Nôm readings of 少; none of them began with /s/ but th (/tʰ/) instead:

thiểu, thẹo, thểu, thỉu, thiếu, thẻo

There is also morphological reason why a preinitial *s- is added before the Vietic *t: it either increases the valency of a verb (of a character other than 少), or creates an oblique deverbal noun (from said unknown character) (Sagart and Baxter, 2012).

少 shǎo &lt; syewX &lt; *[s.t]ewʔ ('few')
少 shào &lt; syewH &lt; *[s-t]ewʔ-s (adj. 'young'; n. 'the youth')

Notice in 少 shào (but not 少 shǎo, your character of inquiry), B–S is confident there is a morpheme boundary between *s and *t (denoted by a hyphen but not a period). This is because *s is likely to be a nominalising agent, creating the sense n. 'the youth', as seen in e.g.:

群賢畢至，少長咸集。（晉·王羲之《蘭亭集序》）
All the literati, the young and the old, have congregated. (Preface to the Poems Composed at the Orchid Pavilion, tr. Wikisource)


While your hypothesis that 弋–代 is analogous to the 少–妙 situation is possible, you need to find more pairs as evidence. B–S obviously does not adopt this in their reconstruction because it is useless in face of Vietic evidence. Whereas this may work in Zhengzhang's system. B–S also did not reconstruct 吵 in OC, which has both “s-/t-” and “m-” readings in Guangyun (and so in Japanese [Go-on: みょう・しょう, Kan-on: びょう・そう] and Korean [묘, 초]). I have yet to find any B–S theory for the concurrence.

Personally, I think Zhengzhang synthesises existing evidence well. But B–S has a more analytical and innovative touch in their reconstruction. Evidence regarding 少 and whatever that it associates with are frequently conflicting, so there is yet a fixed answer.


References

Baxter, William H., and Sagart, Laurent. Old Chinese: A New Reconstruction. Oxford University Press, 2014.

Zhengzhang, Shangfang. Old Chinese Phonology. Shanghai Educational Publishing House, 2003.

Sagart, Laurent, and Baxter, William H. &quot;Reconstructing the *s- Prefix in Old Chinese&quot;. Language and Linguistics, vol. 13, no. 1, 2012, pp. 29-59.