Mr & Mrs Danimirj, I admire your ambitions for your son’s future and the lengths you have gone to including taking all kinds of pot shots at anything you thought might secure your son a very good education. And oh, I admire your self-confessed ‘thick skins’ too in leaving no stones unturned in order to achieve your aim. 
But seriously, you definitely come across to me as a pair of fantastic parents who, in spite of your family circumstances, what, with poor health and limited financial means not to mention an unsecured employment future, gosh, many parents would have given up the ghost by now. . . but not you. Your son is indeed very lucky to have parents like you whose attitude is one of ‘never say die’!
OK, your Eton ambitions are not unrealistic in spite of what your background is. Talking about background, I wonder if your son has any Russian or the former Soviet Union heritage? I ‘ll tell you why later before I submit this post. As you are completely upfront with telling strangers about your detailed and personal family circumstances so as to get help for your son, I’d be upfront too in my suggestions and opinions as to what you should do. I hope you don’t get offended by certain things I might say (because it’s not meant to offend), just that I think sometimes in real life there are situations where the saying, beggars cannot be choosers is indeed very true.
My first posting on this thread asked you what were you expecting from Eton when you applied there taking into consideration your limited means. Actually I already knew the answer - a lot of support and financial help. Yes, this you will definitely get, and more, if Eton thinks your son is worth it. But it will be done on their terms, not yours! Ms Francesca had suggested the New Foundation Scholarship which was exactly the first thing that came to my mind when I first read your post.
OK, but you thought financial help in the form of scholarship/bursary would start at age 10 which was indeed the case until about six years ago. The current NFS replaced the old ‘Junior Scholarship’ which first began in the early 1970’s until around 2009. The JS would guarantee the successful boy his 5 years at senior school, Eton, when he turns 13, and in the meantime Eton would send the boy to a prep school for 2-3 years, any prep school in the land subject to Eton’s approval (they have a list of all prep schools in the nation and they definitely know which is ‘suitable’ and which is ‘not suitable’ [their lingo]). Eton’s expectation is to see its JS going on to win the King’s Scholarship (KS) in his last year at prep school. The success rate of this happening is between 80% and 100%. KS will go to College and the non-KS will go to his guaranteed house (any 1 of 24).
The decision to scrap JS and to replace it with the NFS was not taken lightly. The school had given it many years of thought. For one, the Master-in-College (housemaster of College) was fighting tooth and nail against the Provost & Fellows in their proposal to replace the JS right from the start. College’s (very valid) argument was that the scrapping of the JS would effectively mean the end of (poor) state school boys ever becoming a KS. College would effectively be populated by wealthy prep school boys.
The Governors are not in disagreement with College’s view on this very essential point. It hits right into its guts! After all, the School was founded in 1440 for 70 ‘poor scholars’ who all lived and studied in College. With the supply of KSs from poor backgrounds ended, College would now be populated with 70 posh boys. Founder Henry VI might now be rolling in his grave!
So why are the Governors replacing the JS? The short answer is money. Eton has come to the conclusion that to finance annually, 4 (sometimes 5) Junior Scholars for 8 years each doesn’t make much sense. Eton also has the long term policy to support more poor boys. The money saved from financing a JS for 3 years at prep school can now be distributed more widely to other poor boys, e.g. expanding the Sixth Form Scholarship to take in more boys for 2 years in preparation for their A-levels, etc. A few months ago, the initial target of supporting 70 poor boys schoolwide with 100% bursary had been achieved pre target date. This was a major milestone in the school’s ultimate aim to adopt a needs blind admissions policy.
OP, I gave a long background story about Eton and its current scholarship/bursary policies so that I hope you can now have a clearer picture where you think you might put yourself in this conundrum. For many people out there trying to get a grasp of the whole Eton doo-dah can seem to be running around like headless chickens. Various posters although their intentions are genuine no doubt, are posting unrealistic suggestions. The suggestion to send your son to a prep school now is a non-starter. Who is going to finance you? Certainly not Eton, not any more.
Yes, some prep schools do offer scholarships of one kind or another but not much of a bursary but the money we are talking is more of an insult than an assistance. A previous poster asked a very good question. Even assuming your son did get into a prep school now, is there a guarantee that he would go to Eton or indeed any other public school next?
The way I see it, money is of the essence for you. In my books, only a handful of big name schools can realistically help you and your son. Eton is the one you need to concentrate on. You do seem to have lost your direction a bit. I was very impressed with your lead post saying what your son can do. I’m not surprised Eton was impressed too, that’s the sort of stuff Eton looks for in a boy. Ms Francesca was right. Clear your mind and zero in on the NFS as from now onwards.
But I want you to be under no illusions that success is imminent. Many of the boys who go in for the NFS (previously JS) are of KS calibre. The competition will be extremely tough. Your son is obviously very clever. But from what I see, the pass mark for a certain grammar school you applied to was 220 and your son scored 223 which is just 3 marks over. I’m sure there must be many boys scoring over 223 whose families will have the same ambitions like you. These are the competitions I’m talking about. And they come from all over the country.
I asked at the beginning whether your son has any Russian/Soviet heritage. If he has, he can drastically cut the competition very short by applying to another scholarship offered by Eton - the Tsukanov Scholarships.
In conclusion, I would advise that your son goes to the local grammar for a couple or so years and when the time comes, apply for the NFS [Tsukanov - if applicable] and take it from there. You mentioned about moving schools twice; remember the saying about beggars and choosers? For going to Eton you’re complaining about moving schools twice . . .
listen, others would give an arm and a leg and believe me, some may even kill to get their son there!
Good luck in whatever you choose to do. Feel free to PM me if you wish.