Hello Darren,
No need! Your correction will apply for the next run. For the wrong posting of the previous period, we have a standard functionality under Controlling module>Cost Center Accounting to perform Reposting Documents. So, you select the FI or CO document created from the PP and you have the option to change/modify the cost centers as needed and post it. So, the desired effect will be achieved.
Let me know if this works with you. Thanks.
All the best,
Reda Diab