The insert is outside of the box.
An additional word about gluing styrofoam. Some glues work better than others. I used Weldbond, which is an all around glue that will work with many items. I originally found it mentioned on the website This To That. To glue wood pieces together, though, I pretty much stick to wood glue.
The next picture is a closeup of the oven area and the top of the copper.
I covered the styrofoam and filled in gaps with drywall compound. I've smoothed the compound somewhat, may need to add more here and there.