You can move the selection with Object->Transform->Move. If you calculate the displacement needed for the bounding box of the selection, you can move the selection without grouping it.
From the Info palette (window) you can see the X/Y coordinates and Width and Height. The X/Y coordinates give the upper left corner of the selected objects bounding box. Add half the width to the X and deduct half the height from the Y and you have the center coordinate.
Get the center for the bounding box of the whole selection and of an object that you have centered (in your case the big background square). Then deduct the center of the "centering object" from the center of the selection you want to align and use that displacement in the Move.
Not that this is that easy, but it might be a lot less work than grouping/ungrouping and putting everything back to the original layer. Anyway, it's the best I can come up with
I made an Excel sheet to explain what I mean. Rename the file to .xls and it should work.