WOOO!!! You improved TREMENDOUSLY from that lunge-line lesson you posted before. Way to go!!
I'm just learning to canter, too. Isn't it fun? So much nicer than trotting, although your sitting trot looks pretty good too!
From the vast depths of my three weeks experience at learning to canter... I find that if I keep my weight a little bit "back" and keep my lower back a little bit rounded, I don't jounce in the saddle. Butt stays where it is supposed to (mostly). If I do start jouncing a bit, which happens about 1/3 the time on the upward transition for me, focusing on leaning a little back - not a lot - and consciously relaxing my lower back and hips fixes the problem immediately. Relaxed hips seem to be essential.
On thing my trainer told me that helped is to think of the longest part of my leg not being from knee to ankle, but from hip to knee. She said it helps some people to think of pointing their knee to look at the ground. This doesn't work for me - I wind up tightening my glutes when I do that - but just wanted to throw it out in case it's helpful. For me, just focusing on keeping my hip flexors open and loose was the trick.
+1 on thinking of the rein motion as back-and-forth. My trainer said to let my hands belong to the horse at the canter. It's not like posting at all, where the movement in your arms is up-and-down (opening down as you go up, closing up as you come down). It's much more like keeping contact on the bit at the walk, where you find your arms opening forward and closing back.
The other thing she said that has been super helpful so far is to pay attention to the motion of the canter, and notice when my legs naturally come against the horse. I couldn't, for the life of me, say where that is in the gait, but I can definitely feel it. She said just make an extra squeeze there, when my legs would be on anyhow, when I need to keep the horse going. (And I have to do this a LOT - Huey's out to pasture for the winter, so I'm learning to canter on a Schoolmaster, who is lazy as hell, and has all those wonderful School Horse practices, like dropping his head into the reins and pulling on my hands a lot, while dropping out of the canter into a trot. Huey has the opposite thing - you touch him like you want to canter, and he's going to be off like a shot. Much better, IMO, to be learning this on the School Horse than Big Red the High Speed Freight Train...)