Waltzer is the UK (or possibly European) name for the American Tilt-a-Whirl. One major difference is that the Waltzer has a cover over the cars (so if it rains, you don't get wet), whilst Tilt-a-Whirls are open topped.
Waltzer cars finish (for me), at neck height (when sitting in the car) whilst the tilt-o-whirl cars have a slight dome effect (to keep you dry?).
Maybe you need to look at the Hay Bayler as that has the right up and down motion. You would just need the spinning around of the cars on the "plates" of the track. The picture of the Waltzer in abletudu's picture illustrate these plates nicely.