We report new, sensitive observations of two z ~ 3-3.5 FIR-luminous radio galaxies, 6C1909+72 and B3J2330+3927, in 12CO J=1-0 with the Karl Jansky VLA and at 100-500um using Herschel, alongside new and archival 12CO J=4-3 observations from IRAM PdBI. We introduce a new colour-colour diagnostic plot to constrain the redshifts of several distant, dusty galaxies in our target fields. A bright SMG near 6C1909+72 likely shares the same node or filament as the signpost AGN, but it is not detected in CO despite ~20,000 km/s of velocity coverage. Also in the 6C1909+72 field, a large, red dust feature spanning ~500 kpc is aligned with the radio jet. We suggest several processes by which metal-rich material may have been transported, favouring a collimated outflow reminiscent of the jet-oriented metal enrichment seen in local cluster environments. Our interferometric imaging reveals a gas-rich companion to B3J2330+3927; indeed, all bar one of the eight z >~ 2 radio galaxies (or companions) detected in CO provide some evidence that starburst activity in radio-loud AGN at high redshift is driven by the interaction of two or more gas-rich systems in which a significant mass of stars has already formed, rather than via steady accretion of cold gas from the cosmic web. We find that the CO Tb ratios in radio-loud AGN host galaxies are significantly higher than those seen in similarly intense starbursts where AGN activity is less pronounced. Our most extreme example, where L(CO4-3)/L(CO1-0) > 2.7, provides evidence that significant energy is being deposited rapidly into the molecular gas via X-rays and/or mechanical (`quasar-mode) feedback from the AGN, leading to a high degree of turbulence globally and a low optical depth in 12CO - feedback that may lead to the cessation of star formation on a timescale commensurate with that of the jet activity, <~10 Myr.
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