I'm not agreeing with some of those comparisons there xxxplizit...
Ichijou isn't an airhead, and she most certainly retains full use of her brain at all times (albeit in a twisted by 180º fasion compaired to the rest of humanity).
Himeko... I'd be more inclined to say a cross between Tomo (energetic and generally crazy) and Osaka (being an airhead and not understanding simple things).
Rokugou = Chiyo? Sakaki 'possibly', if you really wanted to make a comparison, but otherwise I don't really see any similarities with any of the Azu crew as such.
Rei I agree with totally, she's just like Yomi
Igarashi, also agree with.
I'll add Becky here, because she would work well as Chiyo. Both in the same age range (Chiyo: 10, Becky: 11), both genius material, both in a higher school than they would otherwise be (albeit in different roles).
edit: and yes, it was the same company that did HIMM