I switched off push on the gmail app and went back to push in native mail.app for my gmail.
It's a work account so its part of gmail exchange and google work. I have had no trouble receiving push messages today. I have received them at the same time my desktop mail client gets them. Often faster than the gmail web interface itself!
I've given up on the gmail app for my personal gmail. I really miss push to the native app on non google apps/work accounts but i'm prepared to accept a 15 min interval. The experience with native mail is much faster and better formatted for good readability.
They will fix the gmail apps ugly scaling but its never really got any faster for me, even with background app refresh. I'm sick of that silly colour loading circle.
So you've also had problems of it not refreshing/pushing in the Gmail app, even though it's supposed to?
I'm attempting to get used to using the Gmail app with my new phone, but I feel like pushes and refreshes aren't working fast or sometimes even at all with the Gmail app.