You are correct about this. I like the native mail app but no push is a deal breaker for me. I was using Mailbox for my Gmail account as it supports push but iOS 8 broke push for them, although they say a fix is coming. I would suggest downloading the Gmail app, as it supports push. Before Mailbox I used the Gmail app only for the push notifications and then used the native app to actually navigate through my mail because I hated the Gmail app. It seems to have gotten better now though. Whenever Mailbox gets around to their fix I would try them (it will also be optimized for 6/6 Plus at that time as well).
do you really need that? I used to think I did, but if your on your computer don't you get the email on that? i took gmail off my iPhone. You could set up a redirect/forward rule in osx mail that anytime you get a amazon mail it forwards it to iCloud mail (that way you get instant notification for when you are away out and about and shopping on your iPhone say). You could even do the redirect online in your gmail account. I found it better to not have all the mail bothering me. Thats why I did it that way.
Oh does Gmail app drain your battery? Did you just have everything forward to iCloud or use a whole new address?
