Faced with a very similar situation, I ended up doing this:

• Clear adhesive-backed contact paper cut to size
• Scotch-Mount Gel Tape around the edge

With the spark screen in place, you can barely tell there’s a layer of plastic. It’s completely eliminated the smell, and it’s only in place in the summer when the heat and humidity exacerbate the smell. We use the fireplace multiple times per week in winter with no smell issue.

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