I understand that it would ruin the story but why not shoot the target in the future and then just send back the dead body? Or with their legs broken? Or drugged?
It seems like a lot could go wrong with sending back live targets. If they escape they could kill those people trying to kill them before they're born or as children.
In the future they have that cool contact-less-taser. Why not use that, or some sleeping pills. They're sending them back gagged, a peg on the nose would do it!