Unless you send a huge amount of email (>100000/day per server) your SMTP software should have no problem retrying servers such as Yaho that throttle messages. In my experience the throttling is bearable with reasonable lists (50000/day should be easy)
Changing the user of messages sent by PHP mail() would, I believe, require changing the user your web server software runs under. If you see an added header "X-Authentication-Warning" you could add "nobody" to your /etc/mail/trusted-users (sendmail systems) but I'm not sure that's a good idea at all. Normally "apache" would be the user the web server runs under. Adding "apache" as a trusted user is risky but not as risky as adding "nobody", which is a user likely used by many other common programs and scripts.
Regards