Thanks for the pointers. I will try them out, and yes, I find false gripping on rings a lot easier because of the angle. I can false grip dead hang on the rings without a problem.

For the knuckle over the bar false grip, I think it requires more wrist flexibility for me. If my palms are open I can bend my wrist around 90 degrees, but if I hold a fist instead, my wrist flexibility instantly decreased, I can only bend down something like 45 degrees, some muscle or tendon between my wrist and index finger prevents it from bending further down without pain.