ZS340
If this is regularly creating problems with ATC; surely you have approached the operator about sorting out their problem.
Some places have their own local procedures. At Italian airports we are not allowed to pushback until final figures are received. With such an incentive - the loadsheet figures usually arrive before the last door close!
I believe that there are changes being made for the FAJS loadsheet operation. A different location is now processing the figures. There will be a period while the new system beds in, but there should be a marked improvement once that is complete.
Fingers crossed.
T'Bug