Oh Dan, I am so very, very sorry. My heart breaks for you & Kim. I know you are doing everything humanely possible to find Jake. Please don't give up hope. He's probably tougher than you realize.
Yes, I have always felt the way Monique does. You should never take your bird outside unless he is harnessed or in a carrier. When they are frightened, they are able to fly like you've never seen, even if they are clipped. Fear does that to them, so Dan, Kim, don't give up. My thoughts and prayer are with you. Please keep us posted when you are able, and thank you for having the strength to share this with us. We are all here for you.