congratulations to your instructor! Boy or girl?
I am not one who can just hop on a work bareback, or even stirrup less, to improve my seat. I could do the stirrupless for a bit, in an arena, but out on the trail, I am not willing to tack any extra chances of falling off, and my age is such that I think much more carefully about that possibility. So, it's easy for some folks to say "ride bareback all day", or ride stirrup-less, but I know my own limits, and i'll figure out a way to work within them.
However, a lungline lesson might help you quite a bit. Either on your mare, or on another heavy horse.
I sometimes start out in half seat at the canter (I am no good at a full two point), and as the hrose settles, and I feel ready, I ease back into a seated canter.
Things that help are to be sure you breathing, and to look up and far off, instead of down at your horse. But, if it makes you feel better, I am working on the same problems you have (except that Z does not run away from the leg). It's just a matter of time and repetition.