JRWM47 Maybe the discharges don't happen at the 6kW rate?
With your 13.5 battery and leaving some margin, for an export between 6:00 and 9:00, you would expect the battery to be empty at shortly past 8:00AM at a discharge rate of 6kW.
Clearly, if there is some DC-AC conversion going on too due to some solar generation, this likely has an impact as well.
With many more schedules now available, you could work around this by setting up a subsequent second export schedule with a SOC trigger condition, and space it 5 mins or so apart from the previous export.