He sounds a fair bit like my little guy (except the good eye contact.) His official diagnosis is autism, but we were told that he would "present" more as having Aspergers as he got older, and that has been very true. You may find the same as well. He got more inflexible as he got older, I'm sorry to say. Though that has improved.
As I so often say, the whole diagnostic process is very subjective. What you say here--"No delay in acquiring language, but strange language patterns such as echolalia, trouble with back and forth conversation, making up words, lots of repeating"--sounds a lot like my son as he was. Some would call that Aspergers, the psychologist who diagnosed him considered it enough of a langauge delay to call it autism.
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Sharing the spectrum with my awesome daughter.