If they're blanking him now, it's because they're still finding him annoying despite his improvements.
People blank others as a last resort, after the person just isn't taking the hint that they don't want to hang out with them. It's no crueller than saying "hi X we don't feel you're a good fit for the group any more and we don't want to be friends any more, can go go somewhere else please" to his face, which is really the only other alternative.
I don't think he should ask one of them out 1-2-1, not if they're all blanking him. It's gone beyond being fixable, they've made their feelings clear and he needs to move on now.
It might not be usual to change schools, but is it possible? A fresh start with people who didn't know him before would be a good thing. Otherwise school is something to be got through and life is what happens outside it. A bit like once you're at work, really. Hobbies, clubs, volunteering, college evening classes for fun or to start learning a trade. Getting out in the world and meeting new people will help cure him of his shyness too.
I'm not prying but if he has some form of learning disabilities or neurodiversity this could just be life, unfortunately. Children can be very inclusive but adults generally are not. What is tolerated at a time of life where everyone is shy, awkward and regularly messing up socially, is less well tolerated as everyone matures and those who don't fit in with ordinary teenage/adult life and the social norms, stand out more.
I'm only mentioning this because he seems to be somewhat lacking in ordinary social skills. It's usual in a group of friends for there to be someone you get on less well with and perhaps wouldn't choose to hang out with if they weren't part of the group, but the reality is everyone tolerates those they're less keen on when in the group and sees those they like best on a 1-2-1 basis more often. So for him to be ousted from the group by everyone, to the point where they feel they need to blank him because he won't go away, his behaviour must have been quite awful. Either that or they're all bullies, but that's not how it's sounding to me.
He's not doomed though, not unless he internalises this, develops low self-esteem and falls into a depression. Meeting new people and learning how to get along with a variety of different people, while he's still in the teenage years and people will still be cutting him some slack for that, could well be the making of him.