I had the same problem, your picture frames aren’t probably picture frames anymore but surfaces with a texture attached. Check if that is the case this problem has already been discus here RH-52353
i can remember having similar issues. the problem as you explained is that acting any kind of changes on the picture frame, will turn the “plane surface” into a higher degree “nurbs surface” with textures. the same is troubling other kind of exports (dwg/dxf and ai) from what i remember
auditing your file it reveals that you are actually using Mac Rhino 5.5.3, which does not print or export images when set to vector at all. i recategorized it for you. maybe check out the wip 6 i think its possible there to print images when set to vector.
hi Andrew, that is a bug which has not been solved yet, the issue is known and there are a few topics on this problem here one for example
generally if you are just asking how to change the draw order you can use SendBackward and SendToBack and the other direction BringForward and BringToFront to clear all use ClearDrawOrder note that this only works for curves and hatches but not for any surfaces or other geometry.