First I would ask if you got a pass through. If not, the arrow could be stopping the entry hole and there may be no exit hole. I've had this happen before. The only way I have found to recover animals like this is to do a LOT of foot work. You may have to walk every inch of the area where you think the elk may have died. However, half a mile seems like a long way for a double lung hit like you described. Is it possible that you may have hit a little further back than you think? Sounds a lot like a gut shot to me. On the other hand, freaky things sometimes happen. A few years ago I made a perfect heart shot on big buck with a rifle. There was not one drop of blood. Luckily I saw the deer drop after about 150 yds. Good luck man, losing an animal is a horrible feeling.

Hunt the thickets