Any time you find yourself struggling with some technique, in this case - strumming, it’s always best to simplify what you are doing at first. So what I would suggest is to just work on hitting the accents of the chords, and worry about all the in-between strumming later. The main strumming pattern of the song accents on beat 1, the and-of-2, and beat 4 of every measure. Try strumming only on those beats, and once the pattern becomes second nature, try adding in a few lighter strums in between wherever it feels natural. There is also no substitute for repetition, so practice often, and eventually, your muscle memory will take over, and won’t even need to think about it anymore.
That move to the A chord in the intro falls on the 4th beat of the bar. Incorporate this move as you practice strumming the accents only. With lots of repetition and hard work, I think you’ll find the move become easier and easier!
Other acoustic songs that I would recommend in this style are Ventura Highway and Change The World, right here on the site!
Hope this helps,