Cable screen terminations for enclosure containing SMPS and instrumentation signal conditioners
I think the reason you haven't gotten any response is that it is hard to give any definite answers and it is a big subject. But here are some pointers. The reasons for shielding (U.S. term, my guess that is same as screening) is either to keep EMI out or to keep EMI in. I think your main objective is to keep EMI out of certain modules and signal lines. Looks like that would be the signal conditioners and the corresponding cables.


Assuming the cables are terminated at the main enclosure, so shielding is established between inside and outside. There are noise coupling between the components inside among themselves. If the level of noise coupling is low enough that it can be tolerated, then nothing much has to be done. Otherwise, additional shielding inside the enclosure can be a solution.
Looks like the signal conditioners are shielded already, so the additional shielding inside would be the two signal cables. So your idea of using screened cable inside is fine. As to termination of the screens, I think in this case, the shielding effectiveness would be more consistent if the screens are terminated on both ends.
Mount the signal conditioner straight to the wall enclosure. In conjunction of terminating the cable screens at both ends, to make the shields one big solid low impedance mass is more consistent than star configuration. 


There should not be issue of ground loop on the shields inside the enclosure. But there are likely to be ground loops with the external components. But if the ground loop current is small and only flow on the shields, it might not affect the signals enough to be a problem.