When I read your description, it sounds like there isn't enough (any?) damping. Re-springing would only help if correct the damping problem at the same time. Maybe there isn't enough oil in the legs?
+1"bouncing" is a damping issue, and is separate (although related) to spring rates - if you change spring rates without addressing the damping you'll just end up with the same bouncing at different frequencies.
How old is the bike? How many miles? Has it ever had the fork oil changed? Are the forkseals in good condition? The service schedule for my vintage of bike says to replace the fork oil every 20,000km/12k miles - if you're a lot over that, the first thing I'd do would be get that done...
big