A simple technique I’ve used when I’ve done something like that is to group the offending areas, as you have done, then scaling (in this case) along the z-axis 10x or more, until a scale command on a pre-selected non-planar area shows z-axis handles. I then grab the topmost handle and drag it up, but then type .001 in the VCB so SU scales it down instead. Exiting the group and scaling the group in reverse, .1 in my example, restores the geometry to a planar condition (according to SU internals) so that deleting the offending break lines leaves you with a plane. On your model, scaling back to original size created additional break lines on the sloped area nearest the bottom of the screen. Those new lines also deleted without issue, leaving a plane.