Having messed around with an undulating road idea, I can confidently say that including up/down movement wouldn't make too much of a noticeable difference.
Lookup tables could be used to quickly calculate a road line's vertical position.
Incidentally, it's not really fair to compare Mansell's framerate to Chase HQ's.
Chase HQ has MANY more road-side objects to process each frame, and yet still manages to be very playable.
Also, Mansell uses a play area of 160x83 mode 0 pixels, which is just over 6.5KB of screen area (I'm not counting the instrument panel in this comparison).
Interestingly, Mansell doesn't use a spectrum-sized screen - it uses the full cpc screen width.
Chase HQ on the other hand uses a play area of 128x128 mode 0 pixels, which equals exactly 8KB.
Considering how much stuff it is throwing around the screen, it's a remarkable effort.
(I'm starting to sound like MacDeath here!)
I always like Mansell's smooth scrolling backdrop though.