Circular staff

[gipsa]

Good morning.
I'm trying to write code that convert a linear staff in a circular one.
My idea is:
-let lilypond write a normal linear single staff
-for each grob, fetch the stencil and their position (x coordinate 
relative to the system and y coordinate relative to the staff) using the 
callback after-line-breaking
-save stencils, x-coords, y-coords in three global list variables (each 
callback add an element to the lists)
-after the end of the Score block put a markup block that plots the 
circular staff and draws all the stencils (with the right translation 
and rotation) calculated from the three global lists

Is it possible to obtain this using global lists? I wasn't able to do 
it. Maybe there is a better solution?
Is it possible to have a single line staff on the top (automatically 
incrementing the page width in order to avoid multiple staff lines) and 
the circular staff below it?

This is the structure of my code (without the global lists):

\version "2.24.4"
\language "italiano"

%TODO: define empty global lists

#(define (trasforma-circolare grob)
; Ricava i parametri
  (let*
    (
      (nome (assoc-get 'name (ly:grob-property grob 'meta)))
      (x (ly:grob-relative-coordinate grob (ly:grob-system grob) X)) ; 
x-coord respect to the system
      (y (ly:grob-staff-position grob)) ; y-coord respect to the staff
      (stncl (ly:grob-property grob 'stencil))
    )
    %TODO: add elements x, y, stncl to the global lists
  )
)

CircularStaff = \markup {
  \fill-line {
    \overlay {

      \draw-circle #20 #0.15 ##f
      \draw-circle #21 #0.15 ##f
      \draw-circle #22 #0.15 ##f
      \draw-circle #23 #0.15 ##f
      \draw-circle #24 #0.15 ##f

      %TODO: read the global lists, convert rectangular coords to polar, 
rotate and translate stencil and print one stencil for each element 
(using map)
      %it is easy to draw stencils here because with \overlay we have 
the reference point always at the center of the circular staff, so
      %we spread the x-coords to an angle from 0 to 360 and we add to 
the y-coord the radius of the inner circular staff line
    }
  }
}

\paper {
  page-breaking = #ly:one-page-breaking
  ragged-right = ##t
  ragged-last = ##t
  indent = #0
}

\header { title = "TITOLO" tagline = ##f}

LinearStaff = \new Staff \relative do' { \time 4/4 \key re \major 
\autoBeamOff
  do4 re8 mi8 fa4. r8
}

\score {
  \LinearStaff
}

\markup \null
\CircularStaff

\layout {
  \context {
    \Score
    \override Clef.after-line-breaking = #trasforma-circolare
    %...
    %for every grob (KeySignature, TimeSignature, NoteHead, ...) add a 
callback
  }
}