Just thinking about it...
If that were going to be done the hard way manually all the timesheets having entries for the KLO project would have to be adjustest and processed as far you would normally do with timesheet.
You can (or somebody) can create a process which first queries the timesheets that have entries for the KLO projecct. The creates XML for XOGing the adjustment timesheets with the desired distribution. adequate error handling and logging.
You could also create a project or custom object field which contains the distribution which is taken into account in the process so that it can be changed in the GUI or changed at a given date with another process.
Technically very possible.