I'm in the process of learning "thumb independence" myself. I know most of the cowboy chords in first position, but I've found it easier to learn thumb independence by holding just one simple chord (e.g. G) and play exercises with various thumb/finger combinations. Switching chords while also trying get down thumb independence just made it more complicated at first. Of course you won't be playing songs right away this way, but it seems to have helped to break it down into small steps. Once you've practiced just holding one fixed chord, try playing the notes of a scale over that one chord by moving just a few fingers on the fretting hand to play the scale notes. And at first, play the notes of the scale "on the beat" so that you are pinching an alternating bass note and each successive scale note at the same time. Playing a bass note and a scale note at the same time seems to reinforce the beat which is what the alternating bass is meant to keep. Looking ahead in the lesson book, syncopation comes next...
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