Chords are an excellent foundation for playing classical because they exist as "patterns" in each of the key signatures. If you know the chords, you'll really "see" them when you start tackling classical music, so you'll realize, "Oh, that's just a repetition of a C, Dm, and E."
LH independence is just a matter of practice. In fact, I'm working on Czerny's 24 for the Left Hand, and the right hand has chords and the left hand the melody and I have a difficult time coordinating the right hand chords to the melody! Learning the piano really has a lot of depth -- just when you think you've got a good grasp, you look at the next piece and say, "Yikes! What the heck is that?!?" Then, practice, practice, practice.
Also, there's no shame in playing "below" level. For years, I stretched beyond my technical abilities to play "harder" pieces and met utter frustration. Now, I've dropped several levels just so I can improve on technique, dynamics, and interpretation. It's a much more joyful approach to playing and the "easy" pieces are sounding spectacular.
In piano there is no going "backwards." Eventually, you'll need to do it all.