Yes, the back panels will compress, but NO they will not get lower on the horse. The tree is shaped the way it is and no amount of breaking in will change it.
Yes, if you scoot the saddle forward it will sit more level, but then the tree will be over the shoulders of the horse, which is not correct. Having the saddle too far forward can cause pain and pinching over time, and shorten the horse's strides or reach.
The saddle is sitting too low on the horse in the proper position. You either need a pad that raises the front of the saddle, or you need a correction pad that adds some thickness at the front. Or, you need to hire a saddle fitter to adjust the flocking of the saddle so it fits correctly.