The upper voice in a staff should be \voiceOne and the lowest voice should be \voiceTwo. Middle voices should be three and four, where \voiceThree has stems up and \voiceFour has stems down.

However, if we try setting the middle voice to be \voiceFour, its rest and tuplet bracket want to go below the lowest voice to avoid a collision. We can fix this by instead setting the middle voice to be \voiceThree, and the stems and tuplet down (with \stemDown and \tupletDown respectively). This works, but the tuplet bracket ends up overlapping with the stem of the lowest voice (just like in your update):

To remedy this, we can horizontally offset the rest with \once \override NoteColumn.X-offset = #2.5:

…
        <<
            {
                \voiceOne
                s4. <do mib>4. <mib solb>4.
            } \\
            {
                \voiceThree 
                \stemDown \tupletDown
                \once \override NoteColumn.X-offset = #2.5
                \tuplet 6/9 {r8 solb,[ lab do sib solb]} |
            } \\
            {
                \voiceTwo
                <lab, lab,>2.
            }
        >>
…

If you don’t like the large horizontal offset, another option would be to change the position of the tuplet beam with \once \override Beam.positions = #'(0 . 0), and to beam over the rest \tuplet 6/9 {r8[ solb, lab do sib solb]}. This will make the tuplet bracket necessary:

The upper voice in a staff should be \voiceOne and the lowest voice should be \voiceTwo. Middle voices should be three and four, where \voiceThree has stems up and \voiceFour has stems down.

However, if we try setting the middle voice to be \voiceFour, its rest and tuplet bracket want to go below the lowest voice to avoid a collision. We can fix this by instead setting the middle voice to be \voiceThree, and the stems and tuplet down (with \stemDown and \tupletDown respectively). This works, but the tuplet bracket ends up overlapping with the stem of the lowest voice (just like in your update):

To remedy this, we can horizontally offset the rest with \once \override NoteColumn.X-offset = #2.5:

…
        <<
            {
                \voiceOne
                s4. <do mib>4. <mib solb>4.
            } \\
            {
                \voiceThree 
                \stemDown \tupletDown
                \once \override NoteColumn.X-offset = #2.5
                \tuplet 6/9 {r8 solb,[ lab do sib solb]} |
            } \\
            {
                \voiceTwo
                <lab, lab,>2.
            }
        >>
…

If you don’t like the large horizontal offset, another option would be to change the position of the tuplet beam with \once \override Beam.positions = #'(0 . 0), and to beam under the rest \tuplet 6/9 {r8[ solb, lab do sib solb]}. This will make the tuplet bracket necessary: