Interesting thread as I think we all have had similar problems, although for some of us (not me), this may have been in the distant past
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JustinGuitar teaches what he calls "One Minute Changes". Using a timer set for one minute, see how many times you can make the required chord changes over and over again. Then do it again and try to beat your "score". Then repeat X 1000 until you are fast enough to do it in time with the song, then apply it to said song. Voila! It has worked for me dozens of times.
I think this method incorporates the idea of starting so slowly that you can't mess up, and working up to speed as quickly as you can. It's like the old adage of how one eats an elephant: "one bite at a time".
Hope this helps.