I might be mistaken (but don’t have time to take a look at the documentation right now) but I thought the originate command treated the channel as the destination and the extension as the source that the destination is connected to. This may be your problem.
What you might want to try is to set your destination channel to something like:
Local/${NumToCall}@from-internal/n
where the number to call is the fully qualified number and the from-internal is what ever context you want to call to go through where the call would normally originate from. This way - if you have any accounting setup or other features - they will all run through as a normal call. (this can be very handy on AAH given all the routing tables and everything that you can setup).