“Shakespeare in the park” was a line that Whedon threw to Downey on the day of filming. Downey then ad-libbed “Doth mother know you weareth her drapes?” Similarly, the shawarma aside came up when he asked Whedon for more material following his revival. The director gave him a few options, shawarma among them, which Downey then took and ran with to its glorious conclusion. Saying that the arc reactor was a “terrible privilege” was also an addition of his that Whedon loved.
One of many great little tidbits. The geek in me is loving this!
The intention was to impart that there are two Hulks within Banner — the first one we see, when the change is out of his control, is vicious and brutal. The second Hulk, the one he chooses to become, is the Hulk who can help the team and catch his friends when they fall.
So my theory was correct, the story I told myself about how this works. Now if Whedon had only just fleshed that idea out a little but more I would have been happy.