You're a braver man that I, Gunga Din. I need the trap to kill them. Once I catch them alive I can't bear to "lose" them. One of the main reasons I use a snap trap. But I don't have rats. Only the occasional mouse. And not since I've had dogs.
I think I know where the rodents are hanging out in our backyard - we have a woodpile which consists mostly of trees that had to be removed or trimmed. It is roughly two cords of wood. We also have ivy in an adjacent corner of the property. Our dog Penny used to climb the woodpile - she was genetically pre-programmed to hunt for rats, but Digby doesn't seem to have as much interest and Dingo doesn't seem interested at all.
That's where they are. Woodpile. And possibly ivy behind. If your rat was small enough to be mistaken for a large mouse, it was a juvenile. They're breeding in there. You need to move the woodpile and restack. And possibly lose the ivy. The best way to discourage rats is to remove their food source and their living quarters. (Have you considered taking the "lost" one back there and showing him to the others as a warning?)
I need to move the woodpile anyway for another project, so that may happen as soon as this weekend depending upon weather conditions (its been hot lately) and other motivational factors. I can't show the other rats the "lost" one. I "lost" it.
Ah, the mystery of the lost rat. I'm not sure hanging the mutilated carcass by its tail near the nest would be very effective, anyway. Sounds to me like you need another 'Penny' dog.
I would like to have Penny back, but I like my two dogs that I have now. Digby has some of the same personality traits that Penny had, but he is a mixed breed, so the rat hunting instincts have been diluted down somewhat. Penny was a purebred Min Pin; originally those dogs were bred to hunt rats in Germany. Digby is a mutant Min Pin.