my method of circle strafing is pretty much like you op, A and D for strafe, hold right mouse button to adjust the camera when you doing it

there is not really technique or "how to" to do so, i think its all about experience in your game time. i mean circle strafing in the very basic is basically target/aim at someone and you just run in circle around them aka orbiting.

for me that kind of thing is pretty much a natural thing to do because iam waaay used to do it like bazillion times back in my time playing counter strike or any fps game where circle strafing is a must when you confronting an enemy.

or maybe you can try the lock on system? the lock on feature pivots you at the target so left and right make you circle it while back makes you backpedal away from it, this works even with legacy.