\version "2.19.49"

% angle brackets cause SVG error so reformat:
% #<Mom 1> becomes [Mom 1]
#(define (reformat-moment mom)
   (let* ((mom (format #f "~a" mom))
          (mom (string-drop mom 2))
          (mom (string-drop-right mom 1)))
     (string-concatenate (list "[" mom "]"))))

% grob name + absolute moment + (system) coordinates should be enough for a unique id...
#(define (get-unique-id grob)
   (let ((sys (ly:grob-system grob)))
     (list
      (cons 'name
        (symbol->string (grob::name grob)))
      (cons 'when
        (reformat-moment (grob::when grob)))
      (cons 'x-pos
        (number->string (ly:grob-relative-coordinate grob sys X)))
      (cons 'y-pos
        (number->string (ly:grob-relative-coordinate grob sys Y))))))

assignIDs =
#(let ((grob-names (map car all-grob-descriptions)))
   #{
     #@(map (lambda (x) #{
       \override #(list 'Score x 'output-attributes) = #get-unique-id
       #})
     grob-names)
   #})
{
  \assignIDs
  a1
  \break
  a
  \break
  a
}