This month I had 3 domestic US flights, booked as codeshares on AA ticket stock. Even under that restriction, I've gotten 2 upgrades.

One thing that does help is to make sure you've got both apps installed/know both websites: Recognize that for the next couple of months, US and AA are still different operating carriers.

I've noticed very few hiccups in the system, all flights have posted/checked-in so far, I've been able to use all my Gold benefits as advertised. Except for the very first day, when I was missing from an upgrade standby list, no trouble that could be attributed to integration issues.