I will go ahead and challenge this- not that you can't be right, or even aren't right in the case of your kids (who I am sure you do a great job of taking care of- this isn't meant to insult you personally), but as someone who was homeschooled and had a very different experience, it's worth having a cautionary point of view- if for no other reason than to illustrate how NOT to homeschool.
First, OP is specifically asking about their child, who is autistic. While I would generally suggest that the average person is incapable of providing an education equal to that provided by a whole school full of teachers, it's often the case that if one child requires more attention than the rest of class, they might benefit more from additional attention and 1-on-1 teaching than they might from having more skilled teachers without additional time to spend. So it is a reasonable suggestion.
I'll start at the end, with the question: can you get into a good university? Sure. I didn't really apply to a lot of universities but I did get a full ride at the best engineering school in the state. It hinged more or less entirely on my GPA and standardized test scores. There's probably a whole book you could write on how poor these criteria are, but that's tangential to my point.
I was homeschooled through high school. In general, it was a negative experience. Primarily, I would say, it was because I didn't socialize much. That's not to say that I didn't have bs activities that my parents came up with, I did. We were a part of the local home school group, I took classes with a group of other home schoolers at what I pejoratively referred to as "homeschooler public school." I even managed to join a sports team for a tiny christian school that couldn't get enough players for a full team (I did enjoy that). I think that probably my parents would have said that I had all the social interaction that I ever needed. But actually I spent days or weeks completely alone. I had essentially two friends, that I saw every few weeks. In high school I basically taught myself all of my classes, then studied and took the tests. It sounds like you're doing things a lot better than that. But this isn't meant to be a critique of you(I don't know enough about what you're doing to even attempt that, even if I wanted to), it's supposed to be a cautionary tale.
I don't know if my experience was "average," but taken from my acquaintances (all home schooled) my results were actually better than average. Many had no outside contact for even longer periods of time, and lived in more isolated areas. Most did very little after high school and then joined the family business. I suppose it's likely that this is a difference between rural Missouri and SF.
>What they didn't have to deal with is bullies in middle school and uninterested adult supervision.
I my experience, that's not really a plus, it's just another overextension of supervision which has become so common these days. The world doesn't stop functioning the same way just because you don't experience it. You just wind up with kids that don't know how to deal with that sort of thing- or worse, try bullying themselves when they think they can get away with it. I personally witnessed this on multiple occasions at ostensibly supervised events where the adults were on the other side of a room or we had gone out back.
My parents were very strict and I was virtually never away from them until after I got a job, but that didn't stop me and my five siblings from breaking rules, instead we worked out systems to help us break our parents rules with no or minimal repercussions. We would have whole fake storylines of what we were doing going on that we would switch to if we got caught and post sentries. The sentries would frequently have codewords so that they didn't get caught helping others disobey. My point, so tangentially made, is that kids sometimes need a chance to interact with others without omnipotent but less than omniscient judges interfering.
In summary, what I am attempting to say is that homeschooling certainly can work well but from my (admittedly quite limited) sampling rarely does. That's not to say you shouldn't do it- just make sure that you want to, and that you're ready to spend the time to do it right.