Gmail with iPhone (Exchange) push & Apple Mail IMAP

Question

Hi, I've managed to get a Gmail account going on an iPhone using the Exchange protocol. Push is working fine. I use Apple Mail to access the same Gmail account via IMAP.
When I reply to a message using the iPhone, the Replied flag (the little 180-degree U-turn arrow symbol) shows up next to the message in iPhone Mail, but this flag doesn't appear in Apple Mail. Likewise, if I reply to the message using Apple Mail, the Replied flag shows up in Apple Mail but not in iPhone Mail.
Basically, I would like push email, but would like the Replied flags to be shown correctly between the email programs.
I've tested this using a few other potential settings with the following results:
* Attempt [1]: iPhone Mail accessing Gmail using the IMAP protocol (no push); Apple Mail using the IMAP protocol (push via IMAP-idle): If a message is replied using the iPhone, the Read & Replied flags are not synced to Apple Mail. However, flags produced using Apple Mail are brought across to iPhone Mail. BUT, if Apple Mail is quit & started up again, the proper Read & Replied flags are shown.
* Attempt [2]: iPhone Mail accessing Gmail using the pre-made Gmail settings (no push); Apple Mail using the IMAP protocol (push via IMAP-idle): Same results as Attempt [1].
* Attempt [3]: iPhone Mail accessing Gmail using Exchange (push); Apple Mail using the Exchange protocol: Can't seem to get Apple Mail working at all. Tried all sorts of settings, but no luck.
* Attempt [4]: iPhone Mail accessing another non-Gmail server using IMAP (no push); Apple Mail using IMAP (push via IMAP-idle): Reading & replying to messages using the iPhone or Apple Mail will always correctly show the Replied flags on the other platform.
* Attempt [5]: iPhone Mail accessing MobileMe using pre-made MobileMe settings (push); Apple Mail using MobileMe (push): Reading & replying to messages using the iPhone or Apple Mail will always correctly show the Replied flags on the other platform.
So the only way to get push email happening with correct syncing of the flags between email programs is to use MobileMe. It doesn't seem possible using Gmail, unless someone can tell me the Exchange server settings for Apple Mail so that it can be tested.

Answer 1

That's the way it works with Exchange, and there's no workaround until Apple fixes it. It's the same for 'regular' Exchange accounts - the replied/forwarded tags applied by the iPhone Mail app aren't seen by Outlook, and vice versa.
You can submit feedback to Apple: http://www.apple.com/feedback/iphone.html.