hairpinWithInsideText = 
#(define-music-function (text) (markup?)
#{
  \once \override Voice.Hairpin #'after-line-breaking = 
    #(lambda (grob)
      (let* ((stencil (ly:hairpin::print grob))
             (new-stencil (ly:stencil-aligned-to
               (ly:stencil-combine-at-edge
                 (ly:stencil-aligned-to stencil X RIGHT)
                 Y CENTER
                 ; Y DOWN
                 (ly:stencil-aligned-to (grob-interpret-markup grob text) X RIGHT))
               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))
             (grob-name (lambda (x) (assq-ref (ly:grob-property x 'meta) 'name)))
             (par-x (ly:grob-parent grob X))
             (dyn-text (eq? (grob-name par-x) 'DynamicText ))
             (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))))
#})

\score {
    \new Staff \relative c'' {
        \hairpinWithInsideText "poco" c1\< |
        c1 |
        c1\!
    }
}