Wall Oven Depth Surprise

New to this venue.

Replacing wall oven. New oven depth off by 1/2 inch, width and height perfect. Couple of issues.

1. Found the junction box located in middle of cabinet
2. Double backing on the cabinet equals 3/4 inches in total.

My only option is to cut out the back of the cabinet to form fit. Then reinsert the thin 1/8 inch back board. If so, recommended tool. I have a dremel and jigsaw?

Should I relocate the electrical junction box higher in the cabinet? This would require cutting away the sheet rock, and putting in plywood.

Any and all thoughts helpful.