I've only seen Part One and haven't read the script, but share your assessment of the first part of part one. I thought the banter at the start went on for way too long and really had me scratching my head and grasping for something that was going to engage me.
I will definitely see Part Two and am encouraged by your assessment of it deepening.
That said, I would suggest seeing at least Act One of Part One if you can. While the first half of Act One was my least favorite part, the end of Act One was by far the highlight for me (Walter's monologue).