"the soundman has absolutely no idea which way the boat is heading"
He should, one ring on the sonar shows relative bearing, the other is slaved to the gyrocompass and shows true bearing with the boat's heading at the top. Most European Navies in WWII used "RED 90" for port beam and "GREEN 90" for starboard beam which was a lot less confusing than 270 relative for port and 090 relative for starboard. OTOH I've met sailors 6 months out of boot camp who still didn't understand the starboard side was relative to the ship's head, and if Bob the Bosun turned around to face aft it didn't swap sides just to stay on HIS right side. Yeah, some sailors really ARE that stupid.
Simplest way to find true bearing after getting a relative bearing report is to look at the sonar, but turn the periscope or TBT (UZO) to the reported bearing and you'll be looking the direction of whatever is reported. Just be thankful the game only models relative and true bearings, and not magnetic bearings, so you don't have to screw around with compass variation math and trying to remember what the hell Can Ducks Make Vertical Turns applies to.