mines?
If this thing is going to sit on top of your sub, pinging away with active sonar, wouldn't it be rather trivial to send out a scuba diver with a mine to attach to it? You could then program this to detonate when the frigate got tired of tracking you and got, say, 100 miles away.
I admit it would take balls of steel to carry on the rest of your tour with a live mine above your heads, but it sounds like it could be a plan.