I don't recall the source, it was some years ago, but there has been research done on sea-migrating salmon and steelhead which proved pretty conclusively that numbers and health of new juvenile fish were tremendously improved when the decaying bodies of the spawned-out adults where left/placed back into the stream. The explanation was that the bodies of the adults, as they decayed in the stream, released a huge amount of nutrients which invigorated the stream ecosystem as a whole, and gave the smolts a greatly increased amount of forage.
Based on that, I'd say that placing the remains of eaten trout back into the stream or lake they came from would be the best solution. Maybe not the prettiest, but the best for the environment. Maybe put the head and guts under some rocks on the bottom?