Whether you think you can, or you think you can't, you're right. - Henry Ford
If you go through life thinking that the world is out to get you, and that you can't do something, because the world isn't letting you do something, then you're going to continually fail, and be disappointed. At least in my opinion. It's very possible that you thinking you're not going to get a job that you're interviewing for is directly correlated to you actually not getting that job. When you don't feel confident, it's externally visible. Mannerisms, speech patterns, nervous twitches, etc. are all factors. People pick up on that kind of stuff, and they immediately think something is off. I'm not trying to be an ass in any way, I just think that a lot of the stuff you're saying is you, and your mindset, and nothing more. Think positive, be positive, right?
My fiance has dedicated her life to autism, just got her masters to be a BCBA. She just has to take the boards in April. She had a suggestion because I talked to her about your woes a little bit. Have you tried recording yourself in a mock interview to see if there's anything in your behavior, speech, mannerisms, etc. that could be impacting the decision to hire you or not? Something that you may notice if you watch yourself, and make adjustments based upon that? I mean, I know companies likely do disqualify candidates based on being on the spectrum, but I can't imagine it's a ton of them. It's actually illegal to do so...
I think this has more to do with your mindset and outlook on things. Hopefully you don't take any of this the wrong way. I'm just trying to help you out. I agree with TI. I think you're putting limitations on yourself before you ever get into the interview, and it's messing things up from the start.
As far as you being socially awkward, I met you and didn't really think so. I thought you talked a ton, but you told me about that ahead of time. Didn't think it was a big deal. Maybe employers get overwhelmed by it? I think the mock interview and recording it is a great idea. Then you have a visual to what all is going on in the interview, and can practice/make adjustments from there.