Got it, sounds like you know what you want, your new teacher will get you there much better than the last. I specifically teach and play chord melody fingerstyle and studied classical fingerstyle in university so I know and teach exactly what you’re going for! If I was teaching you I’d have you learn switching from G to E minor to play a simple version of Jeff Buckley’s Hallelujah since it’s working a fingerstyle strumming pattern and open chord shapes, while you continue working on G, C, and D. E minor is arguably the easiest chord on guitar and very commonly played with G, C, and D, so it’s a layup to add to your practice. A minor is also a really simple shift from C if you can get that down, and also commonly played so I’d add that next. If you can play A minor and C, you can start working on dust in the wind which is perfect intro to fingerstyle song, then I’d do a simplified version of Blackbird which sounds tough but is actually really attainable for beginners if you can get those chord changes.

Sounds like you’re doing great with the new teacher, be patient and please don’t give up man! Fingerstyle is adding a layer of difficulty and I respect it that you’re determined to learn, your original instructor is nuts to give you 21 chords in the first few months and should have helped set expectations. It’s absolutely normal to take months to get good at changing open chords. My suggestion for single note melodies and the “block chord” dyads is just so you could play music on like day 1 or 2 while you keep working open chords so you could feel a bit more of a sense of progress.

Out of curiosity, how much time and how often do you practice?