I think it is important to respect his territory. Sharpie, my veiled, was a lot younger when I got him so this may or may not work as well but this is what I felt made the biggest difference for us.
I never reach in and grab him. Only exception to that was 1× for a vet visit we were going to be late for and 1× that I thought something was really wrong with him. Every time he comes out of his cage its becasue he wants to come out never because he has been forced out. I do have a few little things I know I can do to kind of encourage him to come out. Instead of going in and grabbing him try just leaving the door open. Stay close by of course, but not right next to his enclosure. Give him a little space and maybe a branch or a plant just outside of it that he can get to. Allow him to wonder out on his own when he's ready. I have had him for a little over 3 yrs now & most days he will venture out, some days he doesn't. There are times where he is waiting at his door when I wake up wanting to come out. I think maybe cut back on the number of times you are trying everyday and instead just open his door for an hour or whatever. Anyway...hope this helps some. Good luck.
