Aims. The discovery of large amounts of molecular gas in the hosts of luminous AGN in the local Universe offers a unique opportunity to study its physical conditions under the influence of starbursts and powerful AGN in great detail with present and future mm/sub-mm telescopes. Towards achieving this goal we present first results of multi-J CO line observations of such objects. Methods. We made use of the mm/sub-mm receivers on the James Clerk Maxwell Telescope (JCMT) to conduct observations of the CO J = 3-2, 2-1 lines in five local, optically powerful AGN and of the higher excitation CO J = 4-3 line in 3C 293 (a powerful radio galaxy). Results. Luminous CO J = 3-2 emission and high CO (3-2)/(1-0) intensity ratios are found in all objects, indicating highly excited molecular gas. In 3C 293, an exceptionally bright CO J = 4-3 line with a high CO(4-3)/(1-0) ratio cannot be easily explained given its quiescent star-forming environment and very low AGN X-ray luminosity. Conclusions. In 3C 293, shocks emanating from a well-known interaction of a powerful jet with a dense ISM may be responsible for the high excitation of its molecular gas on galaxy-wide scales. Star formation can readily account for the gas excitation in the rest of the objects, although high X-ray AGN luminosities can also contribute significantly in two cases. Measuring and eventually imaging CO (high-J)/(low-J) line ratios in local luminous QSO hosts can be done by a partially completed ALMA during its early phases of commissioning, promising a sensitive probe of starburst versus AGN activity in obscured environments at high linear resolutions.