The squeak is caused when your finger(s) slide across any wound string. The amount of squeak changes based on how hard you are pressing on the string as you slide your finger from position to position.
Based on your description of how you perform the chord change, my guess is that you are dragging the tips of fingers 1 and 3 across the G and B strings while performing the chord change and/or are rotating finger 2 while still pressing down hard enough to cause a squeak.
So, here are my suggestions:
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Make sure you are lifting fingers 1 and 3 off the strings before changing position,
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Use the least amount of pressure possible to properly fret the strings (squeezing hard is always a bad thing)
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Minimize the amount of movement in finger 2 when doing the chord change
Personally, I find using an anchor finger on the A-C chord change to be harder than simply lifting all 3 fingers, rotating your hand and moving the fingers to the new position, then pressing with the minimal pressure required to get a âno-buzzâ note. I use the same fingering for A that you do (Justinâs preferred method).
YMMV