We used the mm/sub-mm receivers on the James Clerk Maxwell Telescope (JCMT) to observe the CO J=3--2, 2--1 lines in five local, optically powerful AGN and the J=4--3 line in 3C 293 (a powerful radio galaxy). 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 is found which cannot be easily explained given its quiescent star-forming environment and low AGN X-ray luminosity. In this object 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 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. ; Comment: 6 pages, 1 figure, Accepted for publication in Astronomy & Astrophysics