If he's afraid of leaving his cage, I don't recommend forcing him out. Forcing him out could potentially result in cage aggression.
It might be better right now to move slowly around him, and to back off when he's terrified. If you can, whenever you go by his cage, leave him a treat.
When I took Jayde in, a 3 year old rehomed red throated conure, she was terrified of leaving her cage. If I didn't have to handle her, I didn't! Instead, I'd move the cage around the house so she could be "with" me without having to be *on* me. This allowed for her to visit with me without leaving the safety of her cage. After a couple of days, I put a perch on the outside of her cage so if I was sitting down, she could climb down to the perch and be about shoulder height with me, thus yet again being closer. I gave her the choice to leave her cage and now that she's flighted, she just flies to me! Unlike your alex however, Jayde actually *wanted* human interaction, she was just terrified of it at the same time! Talk about confusing behavior!
I also have a wild caught african ringneck that's probably around 3+ years old now. She's been with me for a little over a year now, and before I found out she was wild caught, I was trying to work on gaining her trust. I did this by putting Nutriberries inside her cage as a treat, then would sit up to 5 feet away observing her without looking directly at her. Over time, I got closer to the cage where she would continue eating without flying off. After finding out she is a wild caught import, I kind of "gave up" as I did not feel that she should be a *pet* bird, but an aviary bird with others of her type, since I am unable to take her back to the wild. Even if I could release her where she was captured, I don't know at what age she was captured at, so I don't even know if she knows how to survive in the wild! I just know that her behavior doesn't seem typical for a *captive* raised bird!
A bit over a year later, she's living with my flock of cockatiels in an aviary and I decided to feed the tiels by hand. (aka last week!) I started feeding them millet, which they love and the tiels were flying over to my hand to eat. Now, my tiels range from hand tame and friendly to skittish ex-breeder of unknown age but is over 17 years old. Still, they've learned not to fear me and will eat from my hands - a behavior I started 8 years ago with budgies! I gave the millet to my SO (who is a fish enthusiast, but has a new found love of parrots! :54: ) so he could find the joy in feeding the tiels by hand as well.
Well, Sylphie (the ARN) ended up flying over as well and trying to scare off the cockatiels so she could have some millet, too. Still not trusting of humans, she ended up freaking out and flying away. I decided to try with some seeds instead which brought the tiels over. Sylphie, after watching, once again came over to get some food and attempted to scare the tiels off (the ex-breeder was ignoring her...). After the tiels left, she once again freaked out and flew away! Still, she got within inches of my hand, a behavior she has never shown before! And she chose to do it on her own!
I'm considering continuing the behavior to see if I can gain her trust and get her more comfortable with humans. I'm still thinking she may do best in an aviary situation, but now I'm kind of curious. I started the feeding by hand with 5 adult, flighted budgies that were not tame, just as a little "experiment". And it worked!
[ame="https://www.youtube.com/watch?v=fUx81WHTUwk"]1 Bird in hand Leads to Many - YouTube[/ame]
[ame="https://www.youtube.com/watch?v=AlSm4uFZzVU"]More Budgies!!!! - YouTube[/ame]
And then I had a (previously hand raised then ignored and rehomed) cockatiel that decided she was also interested in this behavior... although it took me too weeks to figure out that's what she wanted! -bangs head against wall-
[ame="https://www.youtube.com/watch?v=q88bN30qOjo"]Sunshine in the Morning - YouTube[/ame]
And when I got another rehomed cockatiel (been in 3 previous homes, don't know if parent raised or hand raised - not tame/friendly), she watched the first one and decided she wanted to participate as well. As you can see, there's quite a huge difference in behavior between the first video and the second!
[ame="https://www.youtube.com/watch?v=R9w9w8nMRmw"]Hesitant Faye - YouTube[/ame]
[ame="https://www.youtube.com/watch?v=rH9ZWxhCSAE"]Not So Hesitant Faye - YouTube[/ame]
Which lead to feeding the rest of the tiel flock by hand as well... (ignore Casey, the third tiel! She's the hand raised one

but the second tiel, the one with the partial bald head is the ex-breeder and father to the first tiel, Sunshine)
[ame="https://www.youtube.com/watch?v=XjKmHswgiHs"]Cockatiel Feeding - April 24th - YouTube[/ame]
Here are a couple of great articles worth reading that may be beneficial.
Working with Fearful Parrots: A Study in Videos | Learning Parrots
Parrot Behavior Myths: Building Trust | Learning Parrots