OK think I'm going to give up on the 970. No-one seems interested anymore!
Today I installed Yosemite 10.10.3 on a clean HD, then installed nvidia driver 346.01.02f04, switched to the nvidia web driver, installed the 970 and as usual got no monitor signal. Screen sharing shows the limited information on the nvidia graphics card that I posted earlier.
Shut down and replaced 970 with original Radeon, started up and weirdly system profiler has 'no information' for the graphics card.
Uninstalled the nvidia driver, restarted, still 'no information' for Radeon.
Reinstalled my Mercury Accelsior pic-e start-up card, started up, and now the Radeon is fully recognised.
I don't think the problem is anything to do with power. It's something to do with the latest nvidia driver, 10.10.3 and this particular model of GTX970.
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One last thing I'd like to try is using an earlier version of Mavericks alongside an earlier version of the nvidia driver. Which versions of each work well with each other and the 970?