Looking at that first picture, the stirrup bars on the saddle could be positioned too far forward for your build. The stirrups are hanging straight down, as they should, but your hips are well behind your heels...though it looks like your seat is close to deepest part of the saddle. That will certainly produce a chair seat and leave you fighting to stay with the motion.
I'm quite tall, but I have the same problem in the saddle my leased horse wears, his owner is the same height I am, but of a very different build and I always feel like I'm fighting the tack to not fall behind. Two point or no stirrups work is easier (imagine that!) because I'm not working against that mismatch between the deepest part of the saddle (where my butt goes) and where the stirrup bars want to put my leg.