Hawking's condition worsened steadily throughout his life. While he was wheelchair-bound by the end of the 1960s, he was still capable of speaking until the 1980s. In the 1970s, he was already an accomplished scientist and would probably have been capable of eating a normal lunch.

The timing would even work for the incident to involve the real Richard Feynman. Though, I can't find anything to suggest the story is true.

It seems that in 1970s when he was at Caltech he already barely could talk, but who knows.

By the late 1970s he was quite difficult to understand, but consider that he began his graduate studies in 1962.