10 tonnes a month...clearly not a B747 operation?
Is the SG you are given correct/ Is it checked shipside with a hydrometer along with the temerature of the uplift fuel? This is the best way to check this? I suspect that this is the issue here? Most fuel companies will do this for you and you can do this yourselves too...
Whilst stated above that the SG of AVTUR is .812....never seen that in my years....seen from 0.785 to 0.820 and every day is different....in USA have seen the highest SGs and in Middle East the lowest (well it is hot!). So check the SG you are using to convert the VOLUME you uplift to a MASS is correct for the location, day, temperature of uplift fuel etc. If you want to do it properly you also need to allow for the SG of the cold fuel in the tank as well....remember this will be colder and therefore heavier and be covering the densitometer in the bottom of the tank thus giving a false reading on the gauge. Some years ago Air New Zealand used to have a graph on the back of their fuel sheet to give an average SG from fuel in tank after fuelling taking in to account the SG/MASS of the fuel in the tank before fuelling, to the Uplifted SG to MASS uplifted so you could give an accurate fuel MASS onboard when checking the actual fuel on board with the fuel sticks.
Frankly having done Fuel Farm / facility audits in a number of places I have found the overwelming majority of the supply companies to be very honest in their dealings and very open to audit of their operations. In fact most are very proud of their operation and wish to demonstrate how compliant with the requirements they are.