Unreliable Syncing of iCloud Email Account

I recently switched from a Gmail account to an iCloud email account in hopes of achieving a better syncing experience across my Mac and iPhone. The push notifications for the iPhone work much better than before, as I see new emails appear on my phone almost instantly. However, my Yosemite Mail app does not receive any push notifications whatsoever. I have to manually open the app and click the "Get Mail" button to see any new emails. I currently have Mail set to check for new messages "automatically".

Another problem is that if I delete or mark a message as read in Yosemite Mail, it will not update on my iPhone until I actually open the app and manually refresh. This makes the unread messages badge rather useless.

Lastly, whenever I compose an email from Yosemite, I have messages that appear in the Drafts folder after the message has already been sent. These messages sometimes need to be deleted several times before I no longer see them.

Does anyone have any advice for improving the usability of iCloud email? Or is this service destined to always be inferior to the good ol' days of the EAS-based Google Sync service for iOS?