It is my understanding that piston rings rotate frantically in a running engine unless something is preventing their rotation, such as a pin. Extreme ovalisation of the cylinder bore will also result in ring alignment, since the rings will eventually find a "most relaxed" position in the bore. I'd definitely get an FE analyst to dig up any block FE results that may be around, and take a look to see what the orientation (phase) of the second-order bore deformation is. If your engine is a Vee, I'm guessing your ring gaps all point inboard or outboard at teardown. (Did I guess right?)
As far as fundamental forces causing ring rotation, I'll list a few possibilities that come to me, but my question for you is "what stops them?" We've probably all seen things rotate for no apparent reason when subject to vibration (Coriolis?).
* bore honing - try as you might, the scratches on the bore surface will probably not be perfectly symmetric. There will likely be some amount of "bore rifling" left, at least until the bore is polished by carbon, etc. Why wouldn't the rings rotate 10deg CCW on the way down and 10deg CW on the way back up? Because there is significant gas loading once out of every four strokes that will overwhelm tension on the top ring (and to a lesser extent, the second)
* gas swirl - there may be some amount of rotation in crevice gas flow
* gap thrust - if the gap is not perfectly symmetric, blow-by and blow-back gases may generate thrust, causing the ring to rotate
* bore lobes - the ring will be jostled around by irregularities in the hot bore shape
* bore ovality (see above)
* piston tilt - not as obvious, but the piston will move around in the bore as the engine runs, and the friction load between the piston and each ring varies over time - there can be a net rotating effect
* Coriolis effect (maybe a stretch)
* momentum - the car will go around corners, maybe the rings don't feel like it (probably a stretch)
More fuel:
I know a gentleman who has run an engine with a viewing glass in the side of a cylinder liner so that he could watch the rings rotate - he said they all rotated, but at different rates.
Instantaneous oil consumption measurements on a running engine showed a correlation between oil consumption spikes and ring gap alignments - but I don't recall the SAE paper where I read that.
Installation issues:
I haven't the slightest idea why people are so picky about ring gap placement when rings are initially installed. Perhaps it's just a tradition that hasn't found its way to the grave. Anybody else have input on that one?