I have found that when I want to change a large number of various items from screen to layer, or vice versa, it is easiest to make a simple VectorScript with the Custom Selection submenu command. (via the Tools menu).
When setting up the criteria for your script, choose "Plane" is "Layer Plane" for one script and "Plane" is "Screen Plane" for another script. Double clicking the ScreenPlane script command will select all of the items that are in the Screen Plane amongst the various objects currently visible.
Once they are selected, even though they might be lines, circles, squares, text, etc? the Object Info Palette will allow you to change their plane orientation from Screen to Layer via a drop down menu "Plane" in the palette. Since they all share this attribute and you custom selected by layer, the Object Info Palette shows a Plane menu item that can toggle from Layer to Screen.
So if you have grouped objects that might contain Screen Plane objects you can either show all classes, explode your groups and change all of the Screen Plane objects to Layer Plane all at once? or, if it's not desirable to ungroup certain groups, you will have to enter each group and execute the script command to select the Screen Plane objects then change them to Layer Plane via the Object Info Palette.
This works for me. Hope that helps. I don't think you can directly change groups from screen plane to layer plane. That would be a cool wish list item though...