Some of the things you describe in your original OP are suggestive of ASD (particularly the hand-flapping) but as you also point out he does not have a typical ASD presentation. However, autism operates along many different dimensions - it's a hypercube, not a spectrum so talking about autistic sprectrum disorder is not very helpful.
You suggest that he is not very well socially motivated. Do you think he wants to make friends with other children? Does he actively seek out their company? Does he want to play in parallel with them? This is a key component.
I would suggest trying to get your LA's Children's Services department to give him an Ed Psy assessment. This might be difficult as he is not clear cut. If you have the budget perhaps think about a private assessment.
This must be a huge worry and I am very sympathetic, I have family experience of autism. The really fantastic news is that he is verbal. the lack of speech and language is the most debilitating thing about autism.
Finally, take heart, my nephew was diagnosed aged 2, no speech and a typical presentation. He is now in mainstream school aged 10, his learning is normal and has effectively been cured of autism. He would no longer clear the hurdle for a diagnosis. Children can 'grow out of it'.