Grace note between arpeggio mark and chord

[Knute Snortum]

Hi everyone.  I have another engraving question.

Without intervention, LilyPond puts a grace note to the left of an
arpeggio mark.  I want it to the right, between the arpeggio mark and
the chord notes.  Here is a snippet of the default behavior:

%%%
\version "2.22.2"

\relative {
  <b d f>4 <g c e> \grace { g'8 } <a, d f>4\arpeggio <g e'> |
}
%%%

(I put in the other chords to show the horizontal spacing.)

How I want it to look is like the attached picture.  (I don't need the
"a" cross-staff.)

Just to show what I've tried, here is an example of one of my
(horrible) attempts at solving the problem:

%%%
\relative {
  <b d f>4 <g c e>4*1/4 \hideNotes <a d f>-\tweak X-offset 3 \arpeggio
    \unHideNotes \once \override NoteColumn.X-offset = 2 \magnifyMusic #2/3
    { g'8 } <a, d f>4 <g e'> |
}
%%%

The horizontal spacing is way off and can never be tweaked to get it
right.  Any assistance would be greatly appreciated.

--
Knute Snortum

grace-and-arpeggio.png
Description: PNG image