Hopefully someone can answer me here, I figured I would keep the discussion open for others to see.
I have been trying to use the pymatgen elastic methods with Quantum Espresso and while trying to get Silicon elastic properties, I noticed that my shear elastic element (C44) was differing from your database by about 25 GPa. After checking convergence criteria, and pseudopotentials, I believe the difference may be in the strains used. The rest of the tensor is within 15% of yours.
I know the filters you apply force different strains to be studied, in your source code, you can specify normal strain and shear strain. However, in your paper you mention that you vary the strain percentages between 0.5% and 1.25% in order to get a consistent elastic tensor. How much do you tend to vary the shear strain (default values in pymatgen are 6%)?
If the suggested criteria of checking ranges of strain and comparing the fits to each other does not work, what other options do I have (besides increasing the kpoints)?
Just to check, you did use the conventional cell for the calculation correct ?