I love this waltz. My professor says "everyone plays that one!" Well they should because it's pretty cool.

I've played it since high school.
Anyway, it sounds like your problem is mostly in the right hand from the way you describe it. Practice this hand under tempo without pedal a few different ways stacatto, shifting accents, accenting each beat and in dotted rhythms. I find playing in stacatto makes it easier to hear any unevenness and takes a bit more motion.
Since the first time in the piu mosso section there is a decrescendo each measure, accent the first note. In the left hand, the bass note should be more pronounced and the inner voices quiet. The second time through marked pp I like to have the bassline as a melody; each of the bottom notes should sound connected through careful pedaling. My edition has a phrase mark over the entire second half of each piu mosso section; the right hand should be very even and quiet the second time. Hope that helps