at the tire width vs the wheel width. Your tire mfgr should recommend a wheel width for your choice.
I'd also look at air pressure. Too low, and the tire will "wad up" and cause the hop.
A look at how the car pitch rotates on launch can help determine why it's hopping. A good video goes a long way, there. The vids will also give insights into tire "behavior".
A set of shocks w/ double setting controls would be a useful tuning tool.
As for the suspension: I'd jack the car up under the axle, putting the stands under the frame. Disconnect the shocks, take out the springs, and see if the axle moves freely thru it's travel.
here'as a link to a very good site for tech help w/ your problem[s]. Billy Shope is one of the best..
http://home.earthlink.net/~whshope/
FWIW, "as Madman says.. Girls squat, race cars don't".

Chuck L.
Hotrodding since 1955.
Injector Inspector.
Turbo Buicks in the 9's...