Mastergammler might referring to a different type of game if it was grid based. Then strafing left or right one "Unit" would be helping if obstacles and walls took up one zone. Then you are sort of playing minesweeper with sound. Right now, the player does not know how much forward, sideward or turning amounts they do. So it's difficult to build a mental map when we don't know the units. You can try to count footsteps but I bet that takes a ton of practice.
Maybe if your left/right sounds added a hum to them instead. Then you might have a constant source to tell you if you are an obstacle or not. Then you could use sonar for longer distances while the humming sonar would be more for obstacle avoidance.