How to make cron send mail from a nonexistent address?

[David M. Karr]

No, I'm not planning on setting up a spam house. :)

I have some cron jobs that send their results to my Gmail account.  I 
read my Gmail in Thunderbird.

I've discovered that Gmail has a "feature" such that mail sent from me 
to me will not be downloaded in a POP request.  I have a feeling that if 
I munge the "from" address of the cron email, this will avoid this 
problem.  I know to set "MAILTO" in the crontab to set where cron sends 
mail to, but I don't see an obvious way to change the FROM address used 
(not surprising).  I would imagine that Google's SMTP probably barfs on 
mail authenticating with one address, but specifying a different from 
address.  I've read about (and used) the information about reconfiguring 
the "/etc/exim4/exim4.conf.template" file to route mail through Gmail 
SMTP, but I don't see anything obvious in those options.