Revolution,
The second link Twat gave is one that deals specifically with your issue. It’s a technique I have been using to resolve this matter when I am faced with it - which is often.
This problem should probably be referred to as something other than “twisting” because it is so often confused with twisting within the hanger. “Drifting” or “listing” might be a better term.
I don’t think it matters at all what type of weights you use - achieving a perfectly symmetrical hang at lower angles is very hard to achieve without somehow stabilizing the hanger.
In that second link I go into how I am often able to get around stabelizing by freeing skin that has snagged within the hanger. This snag occures on one side of the shaft and becomes a temporary “limiting factor” of sorts and forces you to drift or list to one side.
It is safe to assume when listing occurs on different sides one set to the next that uneven skin placement is the culprit and not the larger issue of a genuine internal limiting factor, such as uneven ligament strength and/or length - which is a problem that would make your device consistently list to the same side.
The difficult thing in using the method I describe is mastering the subtlety of it - but I have found it to work perfectly to resolve this problem.
-Cap