Melly and Gully! That's great you took in a rescue! Even greater is that he is doing so well with you.
I too had a "cage bound" bird who was afraid of hands... an Amazon called Ollie. He refused to leave the safety of his cage for 1.5 years, apart from once when he was startled and shot out which ended in disaster as I had to catch him with a towel to stop him hurting himself by flying into walls. Like Gully, Ollie had to be towelled daily for 9 months before he came to live with me so that he could be medicated. The result was that he was terrified of towels and hands. The good news is that with patience Gully can change just like Ollie.
As has been suggested, the first thing you need to do is build Gully's trust in you. There is no rush - you have all the time in the world. That is wonderful he will take treats from you! This is fantastic as you can use the treats to reinforce behaviour you want to see more of. PLUS you and your hands become associated with the treats so Gully will begin to look forward to you and your hands being around.
With Ollie I worked on trust first and being able to approach his cage without him freaking or hiding. As soon as I could get close enough I worked on him taking treats from me. It sounds like you are already at that stage! So then I worked very slowly on introducing Ollie to a hand held perch. I used one that he was used to (it was in his old cage) so that I didn't have to spend too long desensitising him to it. Gradually I brought it closer and closer to him in tiny approximations or steps watching his body language all the time. For each one of those steps I reinforced his relaxed body language with a treat. This took AGES as the only treat he would take from me was a huge palm nut - he could only have one a day so I could only ask for one step a day.
As training went on I discovered he liked cashews so training went faster as I was able to gradually break the cashews into smaller pieces allowing for more behaviour. Anyway I gradually shaped his stepping up on this hand held perch - never pushing him further than he was comfortable with. You can see how I did it here:
Shaping is a wonderful tool to teach any single behaviour without force. Since some parrots have a strong fear response to hands I thought it would be useful to show how to shape stepping up onto a hand held perch. Before we can even begin shaping the step up we may have to introduce our...
theparrotclub.co.uk
I did all this inside his cage. Then gradually I shaped his relaxed body language as I began to move the perch with him on it towards the cage door. Then put him back again. The hardest part was to bring him through the cage door. Eventually we got to his coming through the cage door on the perch, and me turning half a circle and then putting him back again. All this took just under 1.5 years! Then one Christmas he decided to fly out himself and landed on some hanging play gyms across the room. His first taste of freedom under his own steam.
I used to leave the door of his cage open most of the time anyway in case he wanted to try coming out himself. He had outdoor perches to tempt him. He never used them until much later, but all birds are individual. Gully might surprise you and climb out himself. It might be an idea to put a parrot stand nearby for him to climb out on just in case he can't fly. I did this for Bobbie, another of my rescue/rehome Amazons who couldn't fly when she arrived. Even though she learned to fly she still likes to climb out onto the stand and launch herself off it.
Watch Gully's body language all the time (without staring - staring is what predators do before they catch their prey!) and aim to keep it as relaxed as possible all the time. How is he with you cleaning out his cage, or changing the food/water bowls? If he is uneasy, get down low so that you are less of a threat.
Ollie has never got over his fear of hands in that he won't step up on me, but gradually I worked on being able to skritch his head and neck which he loves. If I have to move him, I usually call him and reinforce his coming to me or going into his cage of his own accord. Being hands off has never been a problem.
Looking forward to following your jouney with Gully!
(meant in the best possible way! ) plus i needed someone else in scotland too! 
