Lilypond - Slur arrow-heads changable between left and right side

Question

I found this code for slur-arrows in this question and adapted this answer to make it look nicer.

\version "2.22.0"

slurArrow =
\once \override Slur.stencil =
  #(lambda (grob)
    (let* ((slur-dir (ly:grob-property grob 'direction))
           (right-bound (ly:spanner-bound grob RIGHT))
           (right-bound-stem (ly:grob-object right-bound 'stem))
           (right-bound-stem-dir
             (if (ly:grob? right-bound-stem)
                 (ly:grob-property right-bound-stem 'direction)
                 #f))
           (c-ps (ly:grob-property grob 'control-points))
           (frst (car c-ps))
           (thrd (caddr c-ps))
           ;;; corr-values are my choice
           (corr (cond ((not right-bound-stem-dir)
                        '(0 . 0))
                       ((= slur-dir (* -1 right-bound-stem-dir))
                        (cons -0.4  (* 0.2 slur-dir)))
                       (else '(-0.4 . 0.2))))
           (frth (offset-add (cadddr c-ps) corr)))

      (ly:grob-set-property! grob 'control-points
        (append (list-head c-ps 3) (list frth)))

      (ly:grob-set-property! grob 'line-thickness 0.8)
      (ly:grob-set-property! grob 'thickness 1.2)

    (let* ((orig (ly:grob-original grob))
           (siblings (ly:spanner-broken-into orig)))
       (if (or (null? siblings)
               (equal? grob (car (last-pair siblings))))
           (let* ((default-stil (ly:slur::print grob))
                  (default-stil-lngth
                    (interval-length (ly:stencil-extent default-stil X)))
                  (delta-x-cps (- (car frth) (car frst)))
                  (diff (- default-stil-lngth delta-x-cps))
                  (delta-iv
                    (cons (- (car frth) (car thrd)) (- (cdr frth) (cdr thrd))))
                  (radians->degree (lambda (radians) (/ (* radians 180) PI)))
                  (ang (radians->degree (atan (cdr delta-iv) (car delta-iv))))
                  (arrowhead (ly:font-get-glyph (ly:grob-default-font grob)
                                            "arrowheads.close.01"))
                  (rotated-arrowhead (ly:stencil-rotate arrowhead ang 0 0))
                  (arrowhead-lngth
                    (interval-length (ly:stencil-extent rotated-arrowhead X))))

             (ly:stencil-add
               default-stil
               (ly:stencil-translate
                 rotated-arrowhead
                 ;; Ugh, 3.8 found by trial and error
                 (cons (+ diff (/ arrowhead-lngth 3.8) (car frth))
                       (+ (cdr frth) 0)))))

            (ly:slur::print grob)))))


\relative c'' {
    \slurArrow
    c'4( c \bar "" \break c c)
    \slurArrow
    \slurDown
    c4( c c c)
    \slurArrow
    \stemUp
    \slurUp
    c4( c d a)
    %% maybe add:
    % \shape #'((0 . 0)(0 . 0)(0 . -0.5)(0 . -0.5)) Slur
    \slurArrow
    \slurDown
    c4( a) \slurArrow f( d)
}

Is it possible to define the same arrow-heads for the left side of the slur, so I could use something like:

\slurArrowR for the arrow in the right side (like in the example)
\slurArrowL for the arrow on the left side (Asking how it works...)

---

Edit:

I found a quite more complex example here. There is arrow heads on both sides, enabling to switch the function on and off, but no possibility to change between --> and <--