Hi Grey water, you could add a small aeration system, maybe something as simple as a large fish tank aerator depending on the size of your grey water holding tank. Adding oxygen to your tank will greatly decrease harmful bacteria, while allowing other to strive and digest the waste. Many companies offer aeration system for pools and pond that may also work. If the inlet is too small for a larger aerator, you may want to try with a "hose" type system. Some companies such as ADS have custom aeration tubing that would work for this type of applications. Compared to fish tanks, you will need more air, 2+ SCFM and will require a small compressor.
Generally, grey water with a BOD/TSS of 40 mg/L or less is viable for discharge on the lawn. It is really your E-coli level you want to be careful with. Oxygen should fix your problem.