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.
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