RE: CG Adjustments/Problems
Do as Bubbagates said for the battery to balance the plane.
Now if you don't want to cut the "shiny new covering",
Get some industrial strength velcro. Cut 2 pieces about 2" long. Peel the backing ON ONE SIDE and adhere it to the tape wrapping the foam on the battery. You should have 2 pieces of velcro adhered to the battery.
Next, slide the battery to the proper position needed to balance the plane and make a mark so you know where it goes. Pull the battery out, add a servo extension if needed, remove the backing from the other side of the velcro and put in place and press it in place. To be certain the velcro will not come loose from the balsa, use some THIN CA (I suggest a piece of micro tubing in the tip of a bottle so you can control the amount of CA and get precise placement of the CA) and put a few drops on each adhered strip. If you ever want to remove the battery, reach in and grab it and pull it loose. I have had batteries attached this way stay in place even after a "lawn darting".