\version "2.12.3"

alignGrob =
#(define-music-function (parser location grob-to-align reference-grob dir corr) (string? symbol? integer? number?)
 #{
    \overrideProperty  $grob-to-align #'after-line-breaking #(lambda (grob)
      (let* ((sys (ly:grob-system grob))
	     (array (ly:grob-object sys 'all-elements))
	     (len (ly:grob-array-length array))
	     (current-grob-in-search (lambda (q)
	       (assq-ref (ly:grob-property (ly:grob-array-ref array q) 'meta) 'name)))
	     (default-coord (ly:grob-relative-coordinate grob sys X))
	     (lst '()))

       ;; find all instances in a system of the grob we want to use for alignment
	 (let lp ((x 0))
	   (if (< x len)
	       (begin
		 (if (eq? $reference-grob (current-grob-in-search x))
		     (set! lst
		       (cons (ly:grob-array-ref array x) lst)))
		 (lp (1+ x)))))

      ;; find the grob with the X-coordinate closest to object to be aligned
	(let ((ref (car lst)))
	   (define closest (lambda (x)
	     (if (< (abs (- default-coord
			    (ly:grob-relative-coordinate (car x) sys X)))
		    (abs (- default-coord
		            (ly:grob-relative-coordinate ref sys X))))
		 (set! ref (car x)))
	     (if (not (null? (cdr x)))
		 (closest (cdr x)))))

	  (closest lst)

     ;; calculate offset to X based on choice of alignment
	  (ly:grob-set-property! grob 'extra-offset
	    `(,(cond ((eq? $dir -1) (- (ly:grob-relative-coordinate ref sys X)
				       default-coord))
		     ((eq? $dir 0)  (- (interval-center (ly:grob-extent ref sys X))
				       (interval-center (ly:grob-extent grob sys X))))
		     ((eq? $dir 1)  (- (cdr (ly:grob-extent ref sys X))
				       (cdr (ly:grob-extent grob sys X)))))

		 . ,$corr)))))
  #}
)
\relative c'{
    c d e f |
    \once \override Score.RehearsalMark #'extra-offset = #'(0 . -8.5)
    \once \override Score.RehearsalMark #'baseline-skip = #9
    \mark \markup \center-column { \circle 1 \box A }
    g f e d |
    \once \override Score.RehearsalMark #'extra-offset = #'(0 . -8.5)
    \once \override Score.RehearsalMark #'baseline-skip = #9
    \mark \markup \center-column { \flat { \bold \small \italic Fine. } }
    g f e d |
    \once \override Score.RehearsalMark #'extra-offset = #'(0 . -8.5)
    \once \override Score.RehearsalMark #'baseline-skip = #9
    \override Score.RehearsalMark #'break-visibility = #begin-of-line-invisible
    \mark \markup \center-column { \musicglyph #"scripts.ufermata" \box z } 
}

\relative c'{
    c d e 
    \alignGrob #"TextScript" #'BarLine #0 #-0.75
    f_\markup \magnify #1.25 \box A |
    
    \mark \markup \circle 1
    g f e 
    \alignGrob #"TextScript" #'BarLine #0 #-0.75
    d_\markup \bold \small \italic Fine. |
    
    \mark \markup \flat
    g f e
    \alignGrob #"TextScript" #'BarLine #0 #-0.5
    d_\markup \magnify #1.25 \box z |
    
    \override Score.RehearsalMark #'break-visibility = #begin-of-line-invisible
    \mark \markup \musicglyph #"scripts.ufermata" 
}