I have tried all kinds of picks... grippy dots, star shaped holes, concave picks, ones with flex creases in the middle, ones with actual slots in the middle, clear V-picks, Dava, wooden picks, about every texture Dunlop offers, Jazz III, triangle shaped, round ones, super thick ones, super thin ones, sticky dots you put on the pick, the list goes on and on. My particular deficient technique defeats them all.
I've even tried a standard thumb pick and a couple custom variants. They solves the turning problem, but I have no idea how anyone does anything other than thump the low E string wearing one of those. Yes, I know Johnny Winter was fairly handy with a thumb pick, but I can neither strum chords nor pick out lead lines with 'em.
Amazingly, I have not tried the Cat Whiskers, but they look a lot like the Snarling Dog Brain Picks, which are my favorite brand. The thinnest pick I've tried is .53, which is very pliable... but it still turns. I just ordered some .38 and .46 nylon picks from Dunlop to try, but don't have much hope they'll be the answer, expecting they will be too thin for general purpose electric guitar.
I only have the issue with basic, full chord rhythm strumming, ala campfire style. I have no control issues with turning when playing single notes, double stops, power chords etc.
It's the upstroke of cowboy strumming that gets me. Since I first started out, my normal tendency for comfortably holding a pick is pinching it between my thumb and near the end of index finger, rather than holding it flat against the edge of index finger. DUH! No wonder the pick wants to turn. My natural grip provides little resistance... a small, basically circular area of pressure. I've held it this way for years, and my way of dealing with the turning all these years has been to let the pick slip back deeper into my fingers when strumming chords, so that the tip is barely sticking out, and my fingernails and/or flesh do as much work as the pick, if not more. This does solve the turning problem, but introduces other, equally annoying issues.
It's hard to change... but I"m currently trying to retrain myself to use a more conventional grip, holding the pick flatter against my index finger, but it's been slow going, and I'm not even sure this change will solve my issue. Doesn't really seem like it, so far. A secondary issue I think I have going on is I think I may dig the pick too deeply into the strings on the upstroke, so I'm conscientiously working on that too, as well as trying to improve the angles of attack. Damn, there is a lot that goes on with the simple task of strumming when you start over-thinking it!
Holding a conventional pick with one of the rounded edges pointing at the strings helps, but I just don't like how that feels or sounds. I've also found it helpful if I hold the pick off center a little, and kinda wedge one edge of the pick against the area where the finger and thumb are touching. I have also dabbled with bringing my middle finger into play as RR mentions.
All of these adjustments feel uncomfortable, because I've let the issue persist for so long, hoping it would cure itself over time (as has been suggested by more than one person/teacher). But I am on a mission now to get this sorted out.
I would love to not need be fussy about picks.
It would be great to just be able to grab any ol' pick and have at it.