You have an advantage, because you have recordings which tell you exactly how it should sound, and not only that but you can hear it!
So you can practice this passage in Stages, that is, first play just two chords and play them over and over again until you get the brilliance and evenness that you want. Then add another two chords, and do the same. Repeat until you have mastered the passage.
The important thing here is to visualize playing the chords before you actually do, and also, before you start, give yourself an upbeat, so your body is in the rhythm and relaxed. You can relax a lot easier, be relieved, if you know you only have to play two chords.

Walter Ramsey