True. But I have always had the feeling that XBetza notation should be the vehicle to specify that, not the promotion. What I am missing in XBetza is the possibility to specify a side effect that is mandatory when possible, but not blocking the move when impossible.

How about this: the modifier t is a leg separator like a, except that the actual piece move terminates at that point, and the remaining legs only describe the path of its 'influence'. If this is not a unique continuation, all possible realizations will be combined with the move. So where yacabQ would describe a Queen that (by virtue of the y) does a single King-like burn of an enemy, ytacQ would burn every enemy adjacent to the square it lands on, and can even land there if there is no adjacent enemy at all. An Ultima Pincher Pawn would be ytacfapR, where the captureMatrix would be used to forbid the piece (and its influence) to hop an enemy. Unlike actual moves, the last leg of the influence can be a 'hop-on' leg.

If you are prepared to use JavaScript there are many ways you could interfere with the standard operation of the Diagram. There is for instance a routine ScoreMove(move, predecessor), to prep the 'raw' moves coming out of the move generator by determining the piece types of the capture victims, storing those in the array describing the move, and calculating the effect these captures (and promotions) would have on the score. ('predecessor' is the move preceding it, only used to enforce anti-trading rules). Interfering there to add a few burn victims is not very difficult; you just replace the function by a wrapper for it, like:

var OriginalScoreMove = ScoreMove; // remember the standard routine
var burnX = [ 1, 1, 1, 0, -1, -1, -1, 0 ];
var burnY = [ 1, 0, -1, -1, -1, 0, 1, 1 ]; 
function ScoreMove(m, last) { // and redefine it
  var x = m[0], y = m[1];     // origin
  var piece = board[y][x];    // moving piece
  if(IsBurner(piece)) {
    var n = 4; // 0-3 are the coordinates of origin and destination
    for(var k=0; k<8; k++) {
      var xb = x + burnX[k], yb = y + burnY[k]; // coordinates of neighbor square
      if(IsEnemy(xb, yb)) { // this is assumed to return 0 when (x, y) is off board
        m[n++] = xb; m[n++] = yb; // add a locust victim
        m[-2]++; // this counts the number of squares in the move
      }
    }
  }
  return OriginalScoreMove(m, last); // call the standard routine on the modified move
}