Taking note of advice earlier in this thread, I ditched the existing chemicals and gave the Nova tank another clean with a scrubbing brush and rinsed it thoroughly with copious amounts of running water (in the bath, with the shower hose!).
Then I made up new working solutions from the same bottles of concentrate as the first attempt and had another go at printing. This time, the prints came out dark blue. So I re-did the colour calibration and have now ended up with 'perfect' prints, using exactly the same filter settings as I was using at the start of the year with a different box of paper.
So I have to conclude that the first batch of working solution was not right at all, for whatever reason, and maybe remnants of the initial cleaning process were sufficient to finish it off completely (this is all just a guess really, I'm not a chemist).
As for the 'cyan splashes' on the original test strips, I wonder if these were caused by touching the surface of the paper. The darkroom is in an unheated garage (but an integral part of the house) and was really quite cold last week. Usually I bring the paper into the house to warm it a bit before printing, but I forgot last week and I wonder whether the cold, gloss surface attracted some condensation in the same way that placing fingers close to a cold glass surface can sometimes do.
So the problem has gone away, even if the mystery isn't completely solved. I guess the moral of the story is to rinse very thoroughly indeed after cleaning Nova tanks!