That would place the prealignment of the lyrics into the "seriously
tricky" realm. So it is quite possible that you'll not get any "off the
cuff" elegant solution for this.
A good solution is also constrained by the alignment only being possible
when the lyrics have been turned into stencils, and that happens
depending on the text font defaults at the time of typesetting.
A tedious solution is likely doable where you basically specify
something like
\syllable #1 { Cccc Ccccc Cc Ccc c }
in the first stanza,
\syllable #2 { Cccc Ccccc Cc Ccc c }
in the second stanza and so on: then each stanza would typeset the whole
column, align it, and pick out the right row.