Well I finally sussed it out.

It turns out that as supplied, with all the capacity hat radials untrimmed, the 12M section was resonating nearer 17M, thus causing great confusion. I isolated the 12M section by lifting one end of the loading coil and this enabled me to trim up the 17M section which was resonating 3MHz lower. Having got this working, I reinstated the 12M section, minus a couple of radial spokes and managed to get it in the band.
So the problem seems to be that all the supplied radial spokes for the capacity hats are WAY too long, and the initial resonant frequencies on all bands are nowhere near the frequencies to be expected according to the instructions.