I don’t think b option can help you. It concerns a channel created by the Local channel, and you want the original channel (if I understand correctly). Try Set(__actual-CHANNEL=${CHANNEL}) in contA context and see if you can read it in eagi context. It would work with Dial, I don’t know about Originate.
Note that Answer serves no useful purpose on the B side of originate. It is harmless, unlike on the B side of an incoming call, where it can result in the caller being billed for failed calls.
The A side is already up before the B side is started.