Do you still own your Hawk head - Hawkeye? I too own a Hawk head if you have any questions I may not be able to solve your question directly BUT I can tell you my experiences with mine, which seem similar to what you experienced above.
Hi! I do still have my Hawkhead. He's about 20 years old and I adopted him from a rescue about 4 months ago. My plan is to be his forever home! He is slowly coming around, I am the person he has chosen. He lets me scratch his head now, and loves to chat with me and generally get attention. He is not stepping up yet, he seems extremely scared or upset by seeing hands as well as training targets. We are training now with vocal cues, he sings the song or note I request and gets his treat, very smart bird! I have been getting him used to the position my hand will be in when he does eventually step up, and he's allowing me to get closer slowly without hissing or threatening to bite. I admit I am afraid to push it with him because I've seen the result of a bite from him - it may require medical intervention to say the least. He has had the opportunity to bite me quite a few times and has not, just made the threat.
I would love to hear anything you know that may be helpful! I love this bird and want the best life for him, whatever that looks like.