I use POP on GMail so that I can get mail on my Mac and leave a copy on GMail's server for archive and search purposes, which I do endlessly.

As stated above, Gmail now supports IMAP. The whole point of IMAP is to do what you are trying to do. Keep multiple clients synced to a server, with mail still stored on the server, and every client showing the same messages in the same folders, regardless of when or where you have checked them from.

Go into your Gmail settings, make sure IMAP access is turned on, then add IMAP accounts in Mail.app and the iPhone. I've been doing this ever since Gmail added IMAP and it works very well. No extra accounts needed.