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Kankama said..
Could it not be that the winches are causing it? I think that the self tailers may be putting in a twist. I have been doing a bit of canyoning and abseiling and there is a fair bit if study on how putting rope through a fitting can make a twist occur. I would try it without the self tailers and see if it stops. If so, you may have to feed the rope in with an opposite twist as you ease the sheet.
If you take off the mainsheet and lay it down the deck, coloured fleck(or even the weave) in the rope will help show if it is twisted, the pattern may appear to spiral one way or the other - roll in the opposite direction required till it all 'lines up' straight again, and re- feed.
Having said that, i think Stray is on the money - a non-swivelling block with an appropriate shackle.