Hi Martin,
My suggestion is to use transaction KP97. There are some settings you have to do to limit the copy to only 'actvities and rates'. Go to the Group 'Plan Data'. Select the radio button 'Select Plan Data'. Click the 'Selection' button on the right. You will get a new popup screen. In this screen, select only the options 'Activity quantities' and 'Prices'. Then return to the previous screen.
You can try to execute this in your test system for one cost center only and see if it works as you expect.
Regards
S.Sitapati