Asgorath
Explorer
Yes. My interpretation holds to that belief just as strongly as yours.
What you are attempting to do is say, they could have left off the attack action requirement and then you could have done it anytime. But in my interpretation they can't do the shove anytime. They can't do it if they cast magic missile for example. So them removing any mention of the attack action wouldn't keep things the same as my interpretation. Thus they have to mention the attack action.
Try this: word the feat in such a way that it would allow the shove attack to come before the attacks but only if you took or were going to take the attack action on your turn. After you figure that out then post it and let's see what ya got.
The game has reactions, which can interrupt your turn. Thus, your intention or plan for what you'd like to do later on your turn has no meaning in the rules. Again, JEC explains all of this in detail in the Dragon Talk video on YouTube. As a result, there are no rules like this in the game.