That's an improvement, but lets say something happens, and for some reason you end up falling and landing on your behind with your back tilted in a mostly upright but backwards angle (something I've personally been practicing since I was about 8~9 months old). Where is the head of your hawk going to end up? Probably a little too close to the base of your skull.
If it were me, I'd rig it like an ice axe. At the bottom of your pack, rig a loop which you slide your hawk into just like a hammer in a tool belt, make the loop long enough to accommodate the depth of the hawks head. With the edge pointing to the center of the pack, lift the handle up and attach it to the pack with a tie/compression strap. This captures the hawk, immobilizing it. Now its firmly attached to the pack in such a way as to make it as safe as possible, and still minimize it interfering in your ability to get through brush and branches. Your only concern is if your poll or handle is loose and can fall out, shouldn't happen, but a constricting loop on the handle might help if its a worry.
Erik
PS. Hope you didn't hear Church Lady's voice in your head when you read that.