So, the method of using voiced consonants to represent the yeung tones in Cantonese has already been adopted by Yuen Ren Chao before. The following article describes the original Cantonese Romanization used by Chao, unaltered by Kenneth M. A. Barnett.
Below are the tables of initials.
Like Chao's Gwoyeu Romatzyh, this system uses tonal spelling (the tones are indicated in the spelling). Chao indicates yam tones with voiceless consonants, and yeung tones with voiced ones. The letter "h" has been used here in two senses: to mark aspiration (like in ph, bh and ch), or to imply "voicelessness" (like in mh, nh and lh). In Middle Chinese, the voiced initials are what gave rise to the yeung tones in modern Cantonese. The use of the voiced consonants may thus be considered an homage to that. While the sonorants have theoretically been always voiced, there exist sonorant initials in the yam tone, and these are marked with a following <h>. The exceptions are "i" and "u", which may be interpreted as medials without an initial (or a glottal stop initial), and thus does not carry a voiced initial, hence going into the yam category. While the aspiration mark in the yeung tones is not necessary, since yeung ping and yeung seung are always aspirated while yeung heui and yeung yap are never, it makes the representation more intuitive.
The vowels are a bit more complicated. Chao's analyses is mostly consistent with the later Penkyamp, if you are familiar with the system. The vowel pairs [a]-[ɐ], [ɛ]-[e~ɪ], [ɔ]-[o~ɵ~ʊ] are regarded as contrasting. In addition, [u] and [y] are represented the same way: by <u>, as they do not overlap in Chao's analysis, with the [u] considered as coming after labials (including m-, as in 抹, but not standalone "mu", a point not made clear in his book) or an implied/hidden/elided [w]. Yale yū is written as <iu> (initial i+u) while yīu is <iiu>.
[a] is written as <aa> except when alone, when it is written as <a>, which is used otherwise for the "short" [ɐ].
[ɛ] is normally <ea>, but <e> when alone. <e> is otherwise used for the short [e~ɪ]
[i] is <i>, while <u> represents both [u] and [y]. [u] is used after labials (except for "mu", which lacks a consonant coda) and labio-velars (which creates phonetically [k(ʰ)u], as [k(ʰ)wu] does not exist, considering the lack of phonemic distinction between [ji] and [i] and [wu] and [u]. See also my post where "kwui" is shown in Ball's Romanization).
[ɔ] is <oa>, but <o> alone, which is also used to represent [o~ɵ~ʊ]. Yale's -eui is written as <oi>, while Yale's -oi is <oai>.
[œ] is written as <eu>, and only exists alone or before -k and -ng.
The syllabic nasals are written with a trailing <u>, which may be considered an homage to the Middle Chinese ngu (which becomes ng in modern Cantonese).
On the tones, the level tone uses the normal spelling convention.
The rising tone is written with a trailing x, unless the coda is -i, -u or -ng, in which case they are made "more open" to indicate the rising tone: -e, -o, -g.
The departing tone is written with a trailing h, unless the coda is a semivowel -i/-u or a nasal. The semivowels are written as their consonant letters -y/-w while the nasals are made "heavier": -mm, -nn, -q
For tone shifts, the spelling for the literary pronunciation is used, but an asterisk is added afterwards to indicate it. For example, even though 梨 is read as "lhee" after the tone shift, its literary pronunciation is "lei", and it is thus written as "lei*".
Also, the high level tone may specifically be clarified by adding a trailing <°>.
Chao's system was however, later drastically modified into what could be read as "Barnett-Chao", which you could read about on Wikipedia. In the new system, Barnett dropped the reference to Middle Chinese, and represented the initials in a way more consistent with Cantonese phonology (each initial is only represented one way) and follows the IPA for some of the initials and vowels, though it represents tones with extra silent letters <r> and <h>, making the resulting Romanization very hard to understand. The name of the system would be rendered as "Jrytjryr Romazri" after Barnett's modification, whereas Chao's original system would write it as "Yutyux Romadzih".
