You're doing a fine job here, but there are many details to consider (and some may be a bug or other kind of problem in ATK).
When you perform the force relaxation, the atoms move a bit (not so little, actually), so if you compare the original coordinates that were all 0.5 and 0.825, your relaxed ones are 0.49 and so on. That means, although the lattice symmetry remains BodyCenteredTetragonal, the space group symmetry has changed.
I made some simple tests, and just changing the position of the first atom (Zn) to x=0.00029 immediately causes the symmetry recognition to think the spacegroup is 1 = Triclinic.
We will investigate this a bit further, in particular if it would make sense to optimize the structure with conserved symmetry. But for now, all this means is that your calculation takes a bit longer, the results are in principle correct (note how small the off-diagonal elastic constants are, they can basically be ignored).