A couple of random additional thoughts:

One essential step that enabled me to start making renewed progress at some intermediate stage of learning to counterpoint-pick (especailly in the keys of C and G) was to reconfigure the way I used my left hand to make the basic first-position G chord. I had first learned to put the index finger on the A string, middle finger on the bass E, and ring finger on the high E -- the alternative method is to fret low E with the ring finger, the A string with the middle finger, and use the pinky for high E.

This allows the left hand to remain more still when changing between G and most other chords, and frees up the index finger to play some essential melody notes. It also makes it easier to slide the left hand up the neck to hit, for instance, an "A" on the high E string. Sometimes you might need to slide quickly up to this note and back down, other times you might hit it as part of a D chord made by taking the first-position C-chord-plus-G (fretted with the pinky) and sliding it up two frets. (Since you're fingerpicking and not strumming, you can avoid the open G string which isn't part of the D major chord.)

(All of the above only applies for standard tuning, of course.)

Also: at a much earlier stage of the learning process, I found that the first thing I could do to introduce a bit of variation into my straight repetitive pattern-picking was to "walk" the bass line at each chord change while maintaining my pattern on the treble strings. This may seem counterintuitive -- what you ultimately want to do is to play melody against a steady bass -- but I think it's the easiest and best way to start training your hands to break out of the pattern and begin operating a bit more independently and fluidly.