You shouldn't have any change at all in suspension operation with
larger diameter rim/thinner tire combinations other than considerably
rougher ride and improved steering response due to the stiffer tire
sidewalls.
If you are in fact experiencing handling changes other than above, the
offset is likely incorrect and you no longer have zero offset steering
(ie, bump steer). This can only be corrected by installing rims with
the correct offset to put the centerline of the tire where the factory
rims do.
Also, wider tires will at some point begin to show exactly the same
things, as the impact forces at the edge of the tire get further and
further from the rotational axis of the steering knuckle. No amount of
suspension "rebulding" will have any effect on that, either.
Do NOT use spaces to correct offset, you risk lug bolt failure with the
following probability of wheel separation......
Peter