No, they would have as much mass as the black hole plus the energy of the photons (they still distort spacetime and exert a gravitational force, and have inerti

No, they would have as much mass as the black hole plus the energy of the photons (they still distort spacetime and exert a gravitational force, and have inertial mass) and you still have to move that mass with you. You may have increased your fuel density, but you haven’t reduced its mass compared to antimattter, and you still have not dodged the relativistic rocket equation.