Have you tried starting the 5970 at very low clocks (600-650ish) and waiting for it to heat up? I've got 3 cards that do this (they need reflowed). Once they are up to temperature though (60c+), they run flawlessly at higher clocks.
this is kidna whats happening to one of my 5970, but one of the cores wont accept any load at all (mining) unless the adjacent core heats it up to about 65-70C, then I can start it at normal clock speeds. It's a crappy card anyways though. Master maxes out at 740Mhz @ 1v, slave maxes at 755 @ 1v. Most of my other 5970 get about 770-800ish.
Of the 7 5970's I've gone through (still have 4), only 2 cores couldn't hit 900Mhz @ 1.125... 740 & 755 are really bad. =p
I have one I run at 835-825 @ 1.05v, one at 800 (weak core #1)-845 @ 1.05v, another at 820-820 @ 1.05v, and the last at 820-810 (weak core #2) @ 1.05v. In general, it's about +15Mhz per voltage increase (1.05 to 1.063 to 1.075 to 1.0875 to 1.1), though the 800 one caps out at somewhere between 866-875 (it crashed at 875 twice, haven't bothered going above 865 since then) and the 810 is similar, around 870-880.
The best one can do 950 (140 mem) @ (**ed: 1.150, not 1.250) (unsure past that, the VRMs were around 100 and I wasn't very keen on going any higher on the voltage anyway... the card never went above 70oC though, since ambient was around 25oF..).
I don't mess with them much anymore, pretty much gave up on the hassle of the testing, so they run at something below 1.05 when it's going to be > 70o outside, 1.05 @ <70o, 1.063 @ <60o, 1.075 @ <50o, etc.
I've had a few issues.... (like when the forecast is 55 and it's 68 or something) They could use a nice cleaning but I'll just wait another month or two for that, I guess.
I don't overvolt. I undervolt. Some of us actually have to pay for their electricity.
I pay 6.9c for my electricity.. in general (except for a while after the halving), it's been more profitable to overclock
i would have already sold my stuff off if my elec was >10c (which would have been unfortunate for the last month or so)
ed: oh, as an aside, i suspect I must have read the 1v and somehow got the 1.05v perf 3 base voltage from it. during the summer i ran my 5970's at 0.99v, ~760, due to the heat, not from it being more profitable