  This is the third paper of a series exploring the multi-frequency properties
of a sample of eleven nearby low-excitation radio galaxies (LERGs) in the
southern sky. We are conducting an extensive study of different galaxy
components (stars, dust, warm and cold gas, radio jets) with the aim of better
understanding the AGN fuelling/feedback cycle in LERGs. Here we present new,
deep, sub-kpc resolution Karl G. Jansky Very Large Array (JVLA) data for five
sample sources at 10 GHz. Coupling these data with previously-acquired Atacama
Large Millimeter/submillimeter Array (ALMA) CO(2-1) observations and
measurements of comparable quality from the literature, we carry out for the
first time a full 3D analysis of the relative orientations of jet and disc
rotation axes in six FR I LERGs. This analysis shows (albeit with significant
uncertainties) that the relative orientation angles span a wide range
($\approx$30$^{\circ}-60^{\circ}$). There is no case where both axes are
accurately aligned and there is a marginally significant tendency for jets to
avoid the disc plane. Our study also provides further evidence for the presence
of a jet-CO disc interaction (already inferred from other observational
indicators) in at least one source, NGC 3100. In this case, the limited extent
of the radio jets, along with distortions in both the molecular gas and the jet
components, suggest that the jets are young, interacting with the surrounding
matter and rapidly decelerating.
