Nybom, I am very well prepared to believe that your ds is exceptional. (though no educator in the world can tell you whether he will still, be exceptional in 3 years time)
What I have been saying is that the Local Education Authority has a very limited pot of money to provide the free childcare that comes with fulltime education, so they are not likely to want to do that before the child reaches a certain age. Otherwise, they'd be overrun with parents who all wanted their children to do an extra year at school- because it's an awful lot cheaper and many families on low incomes are financially stretched.
Before your child reaches the set school age, barring the limited hours of free nursery time, it is up to you how you provide for your child to be stimulated.
So there are various alternatives:
You can do it at home - and you cannot make me believe that there are not enough ways of keeping an exceptional child stimulated in a home environment if somebody is able to give some time and though to it.
Your problem is that you have not got the time- so you need to make other arrangements. Your need for uninterrupted time is, strictly speaking, no concern of the LEA's.
If you can find the money, then a childminder might be an excellent alternative. Even a gifted child can have fun playing with other children.
A private school may be another solution- but then of course you will be paying.
If money is short, can you do the rest of your writing in the evenings when he is asleep? Or at weekends and let your husband manage the childcare? As I read your OP, he already does 3 full days at nursery, so we are talking of another 2 days to be found somehow.
(Those Mums who say 'just let the 4yo be bored'- have you ever tried writing a PhD in the company of a 4yo? He would have to stay bored a long time for the OP to be able to concentrate and turn out good research.)
I have plenty of experience of doing research and minding children at the same time and it seems to me that your expectations - both of the system to provide free childcare and of your ds to leave you in peace - are unrealistically high.
I don't think this is about your ds's particular giftedness: I have never met a 4yo who was not demanding or whose needs would sit easily with those of a PhD.
What you should do instead is to arrange a meeting with your tutor and explain the situation and ask what he/she suggests. They have experience - it is not an uncommon situation- and may well have some useful hints.