We've got an unusual mail setup - Google Apps/Gmail in front, with Exim running on our webserver. Mail for any account that doesn't exist in Google Apps is forwarded to Exim. Both of these use the same domain.
Problem is, all mail sent from the Exim accounts (or our PHP app) is only delivered locally, not sent through Gmail.
To perhaps illustrate it better, see this high-quality chart:
[Google Apps] (Tom, Dick, Harry) | v [Exim] (Jane, Mary, Sue)
Mail sent to Jane gets forwarded to Exim by Google. Mail sent to Tom is simply delivered by Google. This is the part that works - the problem is, Jane can't email Tom because as far as Exim is concerned, it runs the whole show.
I'm reading about setting up a SmartHost in Exim, but that requires authentication - and critically, the accounts in Exim do not match those in Apps.
How can I configure Exim to deliver local mail via external routes?