I think a big while loop with three regexp will get you most of the way there.

while (1) {
  /\G<([^>]+)>/gc and do { start_tag($1); next; }
  /\G</([^>]+)>/gc and do { end_tag($1); next; }
  /\G([^<]*)/gc and do { body($1); next; }
  last;
}
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May need an /s modifier on those regexp.