Hi Kev!
As the guide says, ME-to-ERP integration reports the times if you collect ERP distributed labor time. If you've "turned" it off, then you just do not have what to report to ERP because the rest of labor data is ME-native and does not seem to have been meant for direct mapping to ERP labor time - thus the system does not trigger integration in such case, as you observe.
Maybe some custom coding to replace the manual collection with some automated way can help you.
Regards,
Sergiy