They support each other. I think you got a lot of good advice, but knowing you, you probably already knew most of that stuff.
One thing is that bending side to side is connected to bending longitudinally. So, on top of the other bending stuff you are working on, work on getting this hrose to reach way down forward with her neck, then pick up way up, then back up and really lift her shoulders and compress the body, then push her forward, neck out , neck down. LIke a spring, you lengthen and shorten it.
And, as others stated, maybe have someone watch you work with her and see if you really are building in more softness in her by asking for the bending , not giving up til you get it but giving the reward just as soon as you get a good try. Might be hard for you to see these things yourself.
I don't have a ton of experience riding a heavy horse like that, but I think it boils down to you not letting her dullness wear down your EXPECTATIONS from her. I think the duller they are, the duller that we can become because in little ways we give up and settle for less. I know that I do. So, sharpen your expectations for what she can do (within reason for her age/training level) and make yourself stay up there and toe the line with this, and make her meet your there!