I don't have a child on the spectrum, but one of mine was diagnosed with dyslexia and I remember it was difficult for us to figure out which selective school would be sympathetic and most supportive to his needs. Some schools we considered could offer very little in a way of SEN support of any sort, others had 'proper' SEN departments. I am not familiar with North London schools so can't comment on those, but if you haven't checked this out yet, I would do some research first to see which of the schools you have in mind for your DS would be able and willing to provide him with the support he needs. Does any of these schools have children on the spectrum on roll? Are they aware of issues that may arise? Would your DS be able to thrive there?
If you don't have that information yet, it may be worth looking at the http://www.goodschoolsguide.co.uk
website. They have detailed profiles of most selective schools in the country and you should be able to find there some information about their SEN provision (you'd have to subscribe to access the profiles, but there is an option of a 30-day subscription for a reasonable price). I know Tiffin Boys' is not a North London school, but this is what they said about them and their SEN pupils:
Small number have SEN - mostly mild dyses - a few statemented pupils on the ASD spectrum ('we're used to dealing with bright Asperger's boys') and school accommodates with ease. Full-time SENCo plus full-time LSA and one part-time learning support teacher are 'there to support any boys with problems'.
I imagine you would be looking for a school that can say the same as Tiffin's - that they are used to bright Asperger's boys and can provide relevant support.
As for hiring a tutor, I think you have partially answered your own question. You know your DS best and if you suspect that his quirky ways may not be acceptable for most tutors, you are probably right. For me, the first question to ask a potential tutor would be this: 'Would they be happy to take on a very bright boy on the spectrum?' If they don't seem to know what you are referring to, they are probably not the right fit for your DS. I think you would need to look for a tutor with SEN experience, otherwise it may be difficult for your DS to have a good working relationship with a tutor and they would both end up very frustrated.
There is an organisation called PATOSS (Professional Association for Teachers of Students with Specific Learning Difficulties) - they focus primarily on dyslexia but if you ring them, they may be able to help you find a tutor who has experience of working with children on the spectrum. Their contact details are here: https://www.patoss-dyslexia.org/Support ... r-Parents/
If you decide to carry on with DIY tutoring, you will have a massive advantage of knowing the best way of getting through to your DS while a tutor may need some time to 'figure him out'. I would only go for a tutor if I were 100% sure that they would have the right approach for my DS.
Apologies if I'm stating the obvious but I don't know what you have and haven't considered yet. Sorry I can't comment in detail on the specific issue re. tutoring for children on the spectrum, but hopefully someone in a situation similar to yours will reply soon.