How hard is your braking/accelerating? These will induce suspension movements similar to 'undulating road surface', the difference being the first act in opposite directions (the car rotates around its CoG), the second together - both compression or extension (the whole car rises and falls on the suspension). It sounds like you have some suspension steering happening, which might be related to geometry (Mariner's questions), or could be mechanical (bushings, springs, shocks etc). A thorough alignment, without springs and shocks, with a test of the spring and shock functioning seems like a good idea to resolve the questions identified above.
What is your front toe and camber - is that what you describe above? In the short term, I'd dial in some more camber if so (1-1.5* at least), and maybe double the toe-in, and see whether that improves things; that's easily done, and easily reversed if necessary. Even if it improves matters, there may still be other factors involved though - the thorough examination of the suspension is still a good idea.
We all (well I did) drove cars with 70 tyres and I don't remember them being skittish (other terms do spring to mind), and 50/50 weight distribution is supposed to be ideal isn't it?