The old system is not quite as simple. It's onset consonants first, then the tone mark if the vowel is all to the right of the onset consonants, then the vowel, then the tone mark if not already said, than karan. This ใหม่ 'new' is ho hip, mo ma, sara ai maimuan, mai ek.
I don't think the compound vowel symbols are treated as units in the modern system, but spelt out individually, so the เชียง bit would be sara e, cho chang, sara ii, yo yak, ngo ngu - as you type it, which is simpler, and handles anomalous spellings like เทอม 'term', which by the rules should be *เทิม.