I wonder if it would help if you looked at gradient of the SDF as well – maybe you could walk further safely if you're not moving in the same direction as the gradient?
edit: here’s one. I’m not sure this is the one I was thinking of, but I think it does validate your hypothesis that you can reduce the number of steps needed by looking at gradients. https://hal.science/hal-02507361/file/lipschitz-author-versi...