If they are usergroup settings though, they
should be listed under usergroup management. Why are you so adamant that they shouldn't be on the usergroup page, you cause more confusion to the end user by moving around permissions from this page to that page. I would prefer to edit all usergroup settings on the Edit Usergroup page. If you must then you can always duplicate the usergroup permissions for your modification on your own AdminCP page.
I think the "Edit Usergroup" page will drag everything up which is on a "Per Usergroup" basis. You could stick it in the 'misc' group or something like that. You don't need to rotate the wheel...just duplicate the little section of the wheel that you need and stick it on to your page. Although seeing as then you have to engineer all the code to display & process this it seems a bit odd when vB will do it for you! But whatever floats your boat as they say.