We are in a similar, although not identical situation.
Ds1 is 10 and has AS. He is achieving well academically, but like your son homework is a nightmare. He currently has weekly reading, maths and literacy homework. The literacy homework is a mini-project each week. We don't do the reading with him, as it's just not worth the fight. Maths is a weekly battle, but we usually manage to drag him through it. The literacy projects though are a nightmare - he is supposed to do a minimum of an hour, but it can be anything up to 6 or even 8 just to do a one side of typed A4 piece of work.
We have just found out that he has been refused a place at our local academy, on some very shaky grounds, but they could make it extremely hard for us and if they succeed in preventing the LEA from naming them in his statement, given their stated reasons, that will effectively render him unsuitable for any ms secondary.
There is absolutely no suitable ss provision in our area at all. The ss's only take pupils with moderate to severe LDs and although ds's ASD can be a barrier to him accessing the curriculum at times, he actually has no LDs at all.
Have you looked at independent schools at all? Also out of county provision? We are looking at an independent school, which is out of area, but takes a quite a few children with ASD, ADHD and dyslexia and has an excellent reputation for supporting pupils with SNs.
Independent schools tend to have smaller classes, but you do have to look very carefully, as some are highly academic and pushy and/or very sporty. We have been told there are several other children from our LEA that attend the school, but that we will have to prove there is no suitable placement within our area in order to get him a place, which realistically means we are looking at a tribunal.
There is an online directory of independent schools you can subscribe to (although I think you have to pay). Iirc you can search by things like SN support and type of SN etc. Can't for the life of me remember the name of it though. I will come back if I do, but in the meantime try Good Schools Guide
It's heartbreaking isn't it, to realise that there really is no place for them.
If we can't get ds into the independent school we will have no choice but to home school, as if we don't, the LEA will force him into whatever unsuitable provision they have available places for just so that they are fulfilling their requirement to give him an 'adequate education. [angry.