Your style is the total opposite of mine! I love to shift, use those gears! That's why they are there. If I even do too much on the flats in the big ring, in a higher gear, my knees hurt, and I do not have knee issues. I do know about the downshifting before you stand thing, but the thing is, if I am in a really low gear, the hill is probably already so hard that even if I stand, it will feel hard as hell. I've been known to ride at 3 mph on some of the climbs in Europe and I don't care. DH used to stand a lot and has stopped, except on 15-20% grades, which we don't do that much anymore. I can predict exactly when he will stand; at times I can see it gives him a final push, but I just don't have the strength. If I stand, my speed goes *down,* not up, and if I am already going 3 mph, I'd damn well better stay at that. I do tons of leg work, squats, lunges, jumping, etc, so I really think it's just the awkwardness of it, and the fact my legs are short.
2015 Trek Silque SSL
Specialized Oura
2011 Guru Praemio
Specialized Oura
2017 Specialized Ariel Sport