LilyPond outer tuplet bracket alignment

The inner triplet bracket in the first measure here aligns vertically with the lone quintuplet bracket in the second measure.

   \new RhythmicStaff {
      \override Staff.TupletBracket #'staff-padding = #5
      \override Staff.TupletBracket #'padding = #2.25
      \times 4/5 {
         c'2.
         \times 2/3 {
            c'2
            c'4
         }
      }
      \times 4/5 {
         c'2.
         c'2
      }
   }

Is there a way to align both quintuplet brackets vertically?