Pushing while inverted will increase AOA and worsen your situation.....the wrong response, and you only get one shot at this. The appropriate response is "elevator through neutral", as taught by Rich Stowell. Regardless of whether you're inverted or upright, that will reduce AOA.
I think the biggest issue with the so called "moose stall", and the most difficult to simulate in training, is the surprise. There is all kinds of documentation of how long it takes to respond to a true surprise. Firearms training faces the same issue. Stand out there at a range with a pistol holstered, waiting for a target to face is a whole different situation than while you're checking someone's fishing license, he pulls out a pistol and starts shooting.
About the only thing we can do is, as GeeBee suggests, develop a basic set of procedures to perform any time an unusual attitude occurs. So, yes, "Pitch, roll, power" works, but the pitch has to represent stick through neutral, not "push".
Now, understand that in most standard category aircraft, the likelihood of getting upside down is pretty low, but in aerobatics, it's actually a lot higher.
I highly recommend Rich's books and videos, especially, "Emergency Maneuver Training". I also highly recommend flying with Rich if you have the opportunity. He is the "Spin Master" after all. He's done more looking into the "moose stall" and developed procedures to use in the event you get there than anyone I know of. His web site is:
http://www.richstowell.com/
MTV