@ayan2007@AyrtonTwigg @Bishop1964 @classicalMpk @dboing @Demonolith @KingPuzzles @MoistChess @Panagrellus @Sarg0n There is a simple proof of the impossibility of an example in the challenge.
1. A queen combines the power of a rook with the power of a bishop. (Definition, Basic Rule).
2. No advantage obtained by a weaker piece could not be obtained by substituting a stronger piece for the weaker piece in the same position, if the stronger piece includes all the powers of the weaker piece, and if the extra power does not cause a stalemate. (Tautology).*
3. No advantage using a rook or bishop cannot be obtained by substituting a queen for the weaker piece if the extra power does not cause a stalemate (From 1, 2, and 3).
Therefore
4. No promotion of a pawn to Bishop or Rook can be more advantageous than promotion to a queen, if the extra power does not cause a stalemate. (From 3 and definition of promotion, Basic Rule).
*Note: while a knight has less power than a queen, a queen does not include all the powers of a knight. So not every substitution of a knight by a queen will be at least equal in advantage, but every substitution of a bishop or rook by a queen will preserve at least equal advantage, barring stalemates.