The op's ds is 14, he has lagging skills due to dyspraxia, he is school refusing, he is refusing to engage with help. Going down a route of tough love doesn't look like it's had much success so far.
And it's wise not to compare DC, that he's got to 14 doesn't really matter, it's not a case of do this now or live at home for ever, it doesn't work like that.
A diagnosis is an explanation, not an excuse, but can also give clues as to where support is needed. It's also important to understand that he is behaving in this way for a reason, not be a little git, not to get the op into trouble, there will be a reason for him that he can't do this, but he might not be able to identify and articulate why, and if he can't do that, he won't be able to advocate for himself.
Ds1 (ASD, ticks boxes for dyslexia and dyspraxia) was not able at 14 to discuss why he felt the way he did, it's common in neuro conditions for a child to have difficult expressing themselves and identifying why they feel a certain way.
He doesn't yet understand at 15 the full consequences of his actions, so we carry on working with him and finding any examples we can to help him to learn.
If he's forced to do stuff, or if we back off in order for him to do it himself, it doesn't work, we've tried that, on the advice of teachers for years, it doesn't work. If it did work, I suspect he's still be in school, successfully preparing for his GCSEs, instead of us having to take him out to protect his failing mental health.
You can't expect a child to do these things for themselves if they don't have the skills to be able to do them. For some DC, expecting them to engage with a patronising stranger is as big a deal as handing them a complicated flat packed chest of drawers with no instructions and saying "here, do this, you have to finish this within an hour". It can be terrifying, and monstrous pressure, and can be physically impossible.
Not every method works with every child, despite what teachers and CAMHS think!
If the op finds that the "Orange sweet" method works, expecting her ds to take full responsibility without careful guidance and support to,get there, then brilliant, but I hope that if it doesn't work, the op will be sensitive to her ds's needs, and understand that not all DC are the same, and cannot be parented in the same "do as I say because I say so" method that so many advocate.