I am not familiar with the systems to which you refer ..... you might consider that density readings may vary with fuel source (origin) and temperature, the latter being affected by mixing fluids as the aircraft is refuelled.
Do you check the SG with a calibrated hydrometer at all ? If
(a) the measuring device is not calibrated and
(b) you don't replicate the calibration conditions to a reasonable extent
then all bets are off and any reading is only an indication of the value sought, accurate to an unspecified greater or lesser degree.
A target variation of 0.004 is laudable but possibly not readily achievable or repeatable in the field ...... perhaps one of our fuel experts might care to comment ?