It looks like all those semibreves, even if they are changed to a short length, want to take up room because they are a big symbol. If you remove all overrides to lyric hyphens, the syllables come together unless they are smaller than the breve symbol. Changing the X-extent of noteheads makes all the widths dependent on the syllables, but introduces further issues:
\version "2.19.81"
\include "
gregorian.ly"
antiphonText = \lyricmode {
Draw near, Lord, Ho -- ly Fa -- ther,
al -- might -- y and e -- ter -- nal God,
au -- thor of hu -- man dig -- ni -- ty and be -- stow -- er of all grac -- es,
through whom all things pro -- gress,
through whom eve -- ry -- thing is made firm,
who, by the pow -- er of the Ho -- ly Spir -- it,
in or -- der to form a priest -- ly peo -- ple,
es -- tab -- lish a -- mong them min -- is -- ters of Christ your Son in var -- i -- ous or -- ders.
}
aSop = \transpose c c {
%\revert LyricHyphen.minimum-distance
\relative c' {
\cadenzaOn
a'8 \bar"" c\breve*1/1024 \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" \divisioMinima
c\breve*1/1024 \bar"" c \bar"" c \bar"" c \bar"" c \bar"" b8 \bar"" a \bar"" b \bar"" \divisioMaior
a8 \bar"" c\breve*1/1024 \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" b8 \bar"" a \bar"" b \bar"" b \bar"" \divisioMaior
a8 \bar"" c\breve*1/1024 \bar"" c \bar"" c \bar"" c \bar"" c \bar"" \divisioMinima
c\breve*1/1024 \bar"" c \bar"" c \bar"" c \bar"" c \bar"" b8 \bar"" a \bar"" b \bar"" \divisioMaior
a8 \bar"" c\breve*1/1024 \bar"" c \bar"" c \bar"" c \bar"" c \bar"" c \bar"" b8 \bar"" a \bar"" b \bar"" b \bar"" \divisioMaior
b\breve*1/1024 \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" a8 \bar"" b \bar"" c \bar"" b \bar"" \divisioMinima \break
b\breve*1/1024 \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" b \bar"" g8 \bar"" a \bar"" b \bar"" a \bar"" a \bar"" \divisioMaxima
\cadenzaOff
}
}
\score {
<<
\new Staff
<<
\clef "treble"
\new Voice = "sop" { \voiceOne \aSop }
>>
\new Lyrics \lyricsto sop \antiphonText
>>
\layout {
\context { \Voice
\override NoteHead.X-extent = #'(0 . 0)
}
\context { \Lyrics
\override LyricText #'font-family = #'normal
% \override LyricHyphen #'minimum-distance = #1.0
% \override LyricHyphen #'minimum-length = #0.3
%\override LyricHyphen #'minimum-length = #1.5
%\override LyricHyphen #'padding = #0
}
}
}