a simple thing with a 555 as astable and a led could suffice
A 555 as an oscillator would be woefully prone to drift. Far, far worse than the AC mains as a reference.
A quartz reference is required, and this is very accurate, even without any calibration. And the crystal is more stable than the AC mains, so it's not helpful to try to calibrate it from the mains. It's likely to be as accurate at least as a digital multimeter, unless you have access to one from a laboratory that is regularly re-calibrated, so aiming for super-accurate calibration is rather pie-in-the-sky for us mere mortals. However, the uncalibrated error is likely to be far too small to be audible, and probably smaller than the speed error of the cutting lathe used to make the LP.
By my reckoning, key component count would be:
1xquartz crystal, 1xCD4060 divider IC, 1xCD4013 flip-flop IC, 1x ultrabright LED.
I'll put up a plan in a day or so... will draw it up and scan it.
Anyone tried viewing the strobe disc by the light of a television screen (conventional CRT type). That would be a very accurate 60Hz reference - IF it provides enough light. (0r 50Hz in europe/south africa)
(must be a real broadcast - although a DVD player ought to give a very good refence too).