I agree with ecureilx, in terms of general acceptance and awareness things are changing for the better.
I wouldn't worry to much about that.
But on the question should you consider the move from the US here, I would also agree with other posters... don't do it, especially with a teen and a tween!
While local system has made huge improvements to cater to special needs, they cater to locals not expats. Schools like Pathlight are not even accepting application from PR as they are already full/ with wait lists with only citizens.
Only schooling solution viable for expats will be Dover Court ( which has a special needs stream and a mainstream, but the special needs stream is usually full with a waitlist) or sometimes in light cases other
International Schools may take them ( but you might have to lie through your teeth to get through the admission process and not disclose anything and taking the risk of being kicked out when they realise you hadn't been forthcoming.) and you have to imagine that some of those schools are 2000+ students schools, which might prove to be too much in case of sensory issues.
And then there's the question of out of school therapies... if you have deep pockets ( or a good insurance) you may or may not find appropriate therapies...
That's because a lot of therapists that cater to expat kids are expat themselves and come and go. Expect in average to change therapist every year and every now and then one just disappears from one day to the next ( true story), or suddenly all of those who had experience in ASD in teens go back home and you make do with whomever is left...
And so on...
So if you're a long time expat, that your child is used to this, or that you come from a country that's even worse of... Singapore will seem ok... but coming from the US, I doubt that's going to feel like an upgrade.