Well he needs intervention, thats the bottom line. My typical kids don't want to go to school because its boring and holidays are more fun, but they still have to go. What the child ideally wants to do and whats in the child's best interests are rarely the same thing SEN or no SEN.
I hate the 'overwhelm' argument, its a cop out. Overwhelm means I don't know what to do so I am not going to bother trying.
So basically the problem is he doesn't want to be singled out - well the TA could pull him out to a corridor or quiet room and work with him where no-one could see. That would be one solution although not ideal.
The TA also does not appear to have the skills or training necessary. Not surprising, few get much training. She needs to build his interest in her by just playing stuff he enjoys and pairing herself with activities he sees as fun. Then when they have a rapport she can introduce the 'work'. She needs to be working with a set behaviour and reward plan designed by someone with ASD expertise eg using his interests as motivators and rewards. Does he have a token system so if he does some work he gets a reward / points towards a reward etc? That way she can motivate him to do the work.
Some children with ASD will do maths, english, art etc all using their favourite interest eg pokemon. Again thats not a long term solution but it can be a way to get started.
Also does she know when to fade in and out? Good TAs can almost appear like class TAs as they can fade out when needed and so its not like they are obviously glued to the one child. Can he learn in small groups? If so why does she not take a small group with him in it and then he is doing the work and not being singled out. If he can't learn in a small group then that is a good target to teach him to take instruction in a small group.
We do ABA and our tutors are well trained to do all of this and as a result it works well. DS is 4 and he has already been taught how to work in a small group and large group - he has specific targets that have been built systematically eg with his 1:1 fading back bit by bit until now she can often stand outside the room. Of course schools and TAs don't necessarily get that a TA standing outside the room is a success, but the aim should not be that he has a TA forever, but the TA is used to teach him to do it without the TA IFSWIM.
I think you need to approach this as a training issue for the TA - what training has she had / the teacher had? Who is setting the programmes? Is it an autism specialist teacher? Does the outreach team need to come in and demonstrate and work alongside the TA? Do they need to set up clear systematic programmes which the TA can follow? What supervision will the TA have? Who can she go to if she gets stuck? How long does she have to wait for the autism specialist to come in again?
The starting point is how to motivate him to do the work, how to reward him when he does it, and how the TA can gain control and get him to follow her instructions. These are things that the TA should be having guidance on setting up. You can't expect a TA to know how to do this without training and supervision. So I would be making a PITA of myself to the local autism team because otherwise this is money down the drain. Alternatively, the school could buy in supervision eg from a private consultant or ABA (probably unlikely but as more schools become academies I suspect more and more will ditch the LA services as they are often pretty poor quality).
When a 1:1 is well trained the singling out is less of an issue. I know my DS is younger and less aware but his ABA 1:1 is like the pied piper - she is so much fun kids are literally hanging off her legs when I pick him up - they all want to be in DS's small group with her.
If another child said I don't like the teacher and I don't want to be in this class the teacher wouldn't stop doing their job or move them, they would have to work through it. It seems to me she is using your child's disability to suggest its too much for him, when really its too much for her.
You fought for the statement and it has to legally be implemented so they need to find a way of making that happen even if it means spending more on training / supervision.
Also don't expect it to happen overnight. Perhaps this weeks target is 3 lines in the book and next week is 4 etc, just slowly building up and extending the expectation. For my DS its the reward at the end of it thats crucial - if we get that right he will sit for longer and longer eg at 4 he will now work for 15-20 mins and concentrate / follow instructions which is about age appropriate level and he is severe ASD. It has taken 18 months of ABA to get to that point. When we started it was less than 5 seconds.
If the TA is shown how to take data and monitor progress against set targets broken into small steps that should also motivate and reassure her that progress is being made even if it is only tiny steps.