...the motion of a horse galloping etc. during the XC phase has never enabled me to feel as "stable"
Try raising your stirrups about four holes and going for a canter around a field. Your leg won't be able to grip the way it's accustomed to, and you'll be forced to find a new kind of balance. It's OK to rest your knuckles on the crest, but gradually try to take your weight from there and put it into your stirrups.
..."clinic" article by Matt Ryan. In it he said " . . I'll never encourage a rider to grip anywhere ..."
Matt Ryan's advice not to "grip" wouldn't mean don't use your legs to "squeeze". Gripping is clutching to stay in place, which makes the horse tense and happens when your balance is off and/or part of your body is so tense that it can't move with the horse. Squeezing is the selective use of parts of your legs to communicate a message to the horse. At least that's what these words mean in my vocabulary, but I don't get off the farm much.