Hi there and
to the forums!
I think you need to take a step back from "trying" to tame him. Since you've tried a lot of things I think that this is a relationship that's just going to develop naturally. The true bonding comes when he begins to include you in his "flock", and counts you as part of his family. The thing is, that's more than just trust-- he obviously trusts you now, but doesn't feel inclined to seek out time with you. What I would recommend doing is letting him know he's a part of your "flock" first. Do everything in the same room as him--going on the computer, watching TV, hobbies like knitting or scrapbooking or reading--and talk to him as much as you can. I know you're already doing some of this, but making sure to really send the right cues that you'd like to include him in your "flock" will help him connect with you, if he'd like.
Not all budgies are inclined to bond with humans, and if after a while, it seems like he's just not as interested in you as he could be, then you might consider getting him a budgie friend, if you're able to commit to more vet bills, another cage for quarantine, etc.
However, also keep in mind that it may take him a very long time to come out of his shell. My budgie girl and I are bonded to one another but it took a few years for us to really get to a place where we both unanimously agreed on this.
I've had her for five years.
The best advice I can give is to really send all the right body cues-- budgies are very receptive to body language and human emotion. Forget about the "scheduled taming" part of it, since if he gets on your finger on his own, that's already been achieved. The important part is building that bond.
It's not necessary for him to leave the cage, so if he doesn't do so on his own, you shouldn't force him.
Meanwhile, you've come to a great place to learn even more about budgies
Be sure to look through the forum's many Budgie Articles and "stickies", which will ensure you're up to date on all the best practices for budgie care.
If you have any questions after reading through everything, be sure to ask!
We look forward to seeing more of you around the forums!
Keep us posted on how your little one is doing, we'd love to meet him when you get a chance!