I use Nuevasync. It's a $30/yr service that will pull your Gmail via IMAP and push to your phone via Exchange/Activesync, giving you full push capability.
The Gmail account is configured via iOS's Exchange account so it works perfectly with the stock native email app and all other apps/services on the device.
I've been
very happy with it.
Yes, it does require you give up your credentials to a 3rd party company, but I use two-factor authorization and an app specific password, so I can revoke access any time I need to.
http://www.nuevasync.com
(I have no relation to the company other than being a satisfied customer)