Not knowing what size voids or the shape of the bowl.......
You may spend a lot of time turning styrofoam for a tight fit; and then will the epoxy melt the stryofoam?
Depending on the size I would cut a piece of file folder or cardboard, apply CA around the opening on the inside, and add the cardboard layer. Should be stiff enough if the void is not real large.
I did it a few time but at most the voids were about 1" X 2".
Tape as Steve mentioned works well also but the tape must to stick to rough wood. On 2nd thought... maybe the tape is on the outside and you fill from the inside...I think that would work well for a larger void and may be what Steve does.
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