hairpinWithCenteredText =
#(define-music-function (text) (markup?)
  #{
    \once \override Voice.Hairpin.after-line-breaking =
      #(lambda (grob)
        (let* ((stencil (ly:hairpin::print grob))
               (par-y (ly:grob-parent grob Y))
               (dir (ly:grob-property par-y 'direction))
               (new-stencil (ly:stencil-aligned-to
                 (ly:stencil-combine-at-edge
                   (ly:stencil-aligned-to stencil X CENTER)
                   Y dir
                   (ly:stencil-aligned-to
                     (grob-interpret-markup grob text) X CENTER))
                 X LEFT))
               (staff-space (ly:output-def-lookup
                 (ly:grob-layout grob) 'staff-space))
               (staff-line-thickness
                 (ly:output-def-lookup (ly:grob-layout grob) 'line-thickness))
               (par-x (ly:grob-parent grob X))
               (dyn-text (grob::has-interface par-x 'dynamic-text-interface))
               (dyn-text-stencil-x-length
                 (if dyn-text
                   (interval-length
                     (ly:stencil-extent (ly:grob-property par-x 'stencil) X))
                   0))
               (x-shift
                 (if dyn-text
                   (-
                     (+ staff-space dyn-text-stencil-x-length)
                     (* 0.5 staff-line-thickness)) 0)))

        (ly:grob-set-property! grob 'Y-offset 0)
        (ly:grob-set-property! grob 'stencil
           (ly:stencil-translate-axis
            new-stencil
            x-shift X))))
  #})

hairpinMolto =
\hairpinWithCenteredText \markup { \italic molto }

hairpinMore =
\hairpinWithCenteredText \markup { \larger moltissimo }

\layout { ragged-right = ##f }

\relative c' {
  \hairpinMolto
  c2\< c\f
  \hairpinMore
  c2\ppppp\< c\f
  \break
  \hairpinMolto
  c2^\< c\f
  \hairpinMore
  c2\ppppp\< c\f
}