Ewan,
The previous posters have all offered good suggestions, and they're well worth trying -- particularly the soapy water, as the beads sometimes catch prematurely before they seat fully under the bead.
The 1cm of runout is pretty extreme, making me think a section of tube is caught beneath the bead. You didn't mention where the high spot is, but this can sometimes happen if the valve is not fully seated in the rim.
That said, I have noticed all my Duremes do have some native wobble (see:
http://www.thorncycles.co.uk/forums/index.php?topic=3861.0 ) compared to Supremes, Marathon Deluxes, or other tires by different makers. It hasn't been to the same degree as yours, and is not noticeable while riding, but it is still there, worse on my rigid beads, still present on my folders.
Best of luck on the reseating; please let us know how you fare.
Dan.