To answer the initial question on solving the bearing ambiguity: 'Wag your tail'
Sorry guys, a layer is not going to differentiate between two bearings. If you change depth the sound on both directions are going to disappear simultaneously. Because it is the same sound. It's just that the TA sensor can't tell the difference between left and right. I know, it sounds stupid with all that modern technology. But it is just the physics/math of it. And a uuv solution is way to expensive resource wise.
Turn to a different course (a couple of tens of degrees to show it good) and see the mirror 'not real' contact shift in bearing twice as much as the course change (eventually). Since the angle between your tail (TA) and the true contact changes, the angle to the mirror contact must match (on the other side) after the turn. Which causes the sound to appear from a different direction twice as far.
This link shows a picture why it can't tell left from right (about 80% of the page down):
http://www.fas.org/man/dod-101/navy/...ys/asw_sys.htm