I have piano hands too and there's a photo of me somewhere on my old pony with "broken wrists" - ah hands, they never do what we want them to. Um.
You want to carry your hands with your elbows at your sides. Don't spill the coffee mugs! You're ducking a little and seem to be ahead of the movement over your fences and tipping forward a tad on the flat but not very much.
Your knees are gripping your saddle and causing your lower leg to swing back over your fences, I do that too. It's very common. If you open your thighs a little and consciously think about trying to keep your heels anchored to the ground and your leg more forward it will help. Duck feet are a cause AND an effect of pinching knees, and you'll find if you fix those feet your knees and thighs will improve. Yours aren't bad though, mine are about there now and I've been working on them for MONTHS.
It's really interesting reading the different advice offered. My coach is constantly telling me off for relying on Monty's crest/mane, but that might be because I tend to duck a little and by leading UP and forward with my hands, my upper body follows and I don't duck as badly. It's the complete opposite of MudPaint's advice which is to use the crest as a "marker" if you will and place your hands in a particular spot on the horse's neck over each jump until you've landed and can re-establish contact.
I hope I'm not upsetting you by mentioning this - but please don't jump in a standing martingale. I know yours is adjusted loose but I just feel like a running martingale is much safer. I don't know if you ride hunters or jumpers, though, and a standing is a much cleaner look for the hunter ring if that's what you ride. So take my advice as coming from a purely jumpers rider (we don't have hunters here in Aus, not in the sense the USA does at least) and apply it only if it's applicable to your discipline.