Figuring out the mellotron part actually helpt in figuring out the one piano chord I was missing for this section. For the most part, I learned the piano part from a vocal/guitar/piano book of Zombies songs from the Alfred Publishing Company. They said it's a Ddim7, but this didn't sound right to me. I knew the note in the bass register was a D, and this mellotron plays a G# on top of it, so while I'm still dubious about the 7th, I guess it really is a Ddim chord.
The mellotron part for the third verse is a little different, and I don't have that yet. I think the first half is the same though.