It just takes practice. Back when I played bass in a band it always took practice to learn new songs, even songs that looked/sounded "easy". Granted, some songs took less time to learn than others. Sometimes it took something really simple to progress in a song. That thing was to just relax. Your fingers should know where to go for most chords, but if you're concentrating too hard on the chords, your fingers get a bit "stupid". But if you relax you may have some startling results.
I know that when I'm not actively concentrating on practicing chord changes they tend to go easier.
It works for me, maybe it'll work for you too.
What is this "strumming" of which you speak?
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