It's going to be hard for any position to be "natural" if the king is out and roaming about, so I presume that you mean that the position must be legal. Also, as far as I understand it, the king may only teleport in a checkmate position, and not while in check, because otherwise it would be nigh impossible to give a mate.
Firstly, it is entirely possible to get eight queens on a board for checkmate without drawing, like so, with a little help from other White pieces. While this can be done with just the pawns alone, the extra pieces are need to do it in exactly eigth moves.
[FEN "8/PPPPPPPP/8/8/8/8/k7/1RN1K3 w - - 0 1"]
1. a8=Q+ Kxb1 2. c8=Q Kb2 3. d8=Q Kb1 4. e8=Q Kb2 5. f8=Q Kb1 6. g8=Q Kb2 7. h8=Q+ Kb1 8. b8=Q#
But it is also possbile to achieve this effect with just White's eight starting pieces. I remebered this old problem by Josef Kling that does it. The stipulation reads: White checkmates in 14 moves but only after attacking all 64 squares." I would suppose that this position is more "natural" than one with eight White queens.
Do note that while the stipulation reads “64 squares,” it has been proven, that with opposite colored bishops, the starting pieces can only control 63 squares. Kling knee that for sure-it’s just a minor discrepancy that he used “64” to have a better sounding stipulation in my opinion.
[Title "Josef Kling, The Chess Player's Companion 1849, 'Fancy Sketch'"]
[FEN "4k3/8/8/8/8/8/8/RNBQKBNR w - - 0 1"]
1. Qd6 Kf7 2. Rh8 Kg7 3. Bb2+ Kf7 4. Qa6 Ke7 5. Bh3 Kf7 6. Ke2 Ke7 7. Kd3 Kf7 8. Bd4 Ke7 9. Nd2 Kf7 10. Ne2 Ke7 11. Rg1 Kf7 12. Nc3 Ke7 13. Nd5+ Kf7 14. Be6#