Earlier quoted context omitted.
What if we instead look at the last clip as “the one shot” Personally I don’t think that takes anything away
Well, he is standing still, the camera is stationary. For just that last segment, it is easy to answer "how did he do it?" Write out his remarks, rehearse with a timer, then figure out at what point in the countdown to begin speaking. The main thing is that he has say basically one sentence right in a single take, but he is a seasoned television announcer, so that in itself is not too surprising. The much longer segm…
But I think it's about 120 degrees to the left from where they shot the shot of Burke walking. They absolutely had to set up a different shot to get Burke and the Titan III in the same shot.
As an aside... That Saturn V is no longer at that location. Several years ago they moved it a mile to the north and built a building around it to create the Apollo / Saturn V center. Or at least I think it's the same artefact.