Repeat D.S. al fine, but the Fine is in a nested volta

[Knute Snortum]

I'm trying to get a Fine on the first ending of a repeat volta nested in a
repeat segno.  An MWE will probably be clearer:

\version "2.24.3"

music = \relative {
  \time 3/4
  \partial 4 c''4 |
  c c c |
  \repeat segno 2 {
    \bar "||"
    d d d |
    e e
    \repeat volta 2 {
      e |
      f f f |
      \alternative {
        \volta 1 { g g } % I need the Fine here...
        \volta 2 { a a a | }
      }
    }
    \volta 2 \fine % ... not here
    \volta 1 {
      f f f |
      g g g |
      \bar "|."
    }
  }
}

\new Staff \music
\new Staff \unfoldRepeats \music

I am new to the repeat segno syntax, so I'm hoping I just haven't found the
right magic.  I'd like the MIDI to be correct -- I can always fake a "Fine"
if I need to.

--
Knute Snortum