I'm not a paper rules player, but as a former ASAC I'll share what I can about helo ops in ASW. I'll date myself here and say that I controlled SH-2 LAMPS and SH-3 dipping helos, along with S-3s, P-3s, and JMSDF P-2s.
One thing to remember is that an ASW helo is not a search platform. It's a localization/attack platform used once a target has been detected by other means. Once a sub threat was detected, the LAMPS or Dipper would be vectored in to pinpoint the target's location and also try to identify it. With a LAMPS, I'd order buoy drops around the suspected location, normally a pattern of 4 passive buoys. If an SH-3 was available, I'd have a dipping sonar available as well. MAD detection was available from both types of helos as well.
Once a contact is firm enough and rules of engagement are met, a torpedo drop can be made. My own preference during ASW exercises was to vector the helo over the contacts track stern to bow and release the weapon when the MAD needle swung. This places the weapon ahead of the target due to balistic travel after release and in an optimum position to aquire.
Hope this helps. If not, it was fun thinking about those days again.