Repair Laminate with Simple Mat?

I am working on giving a marble look to my kitchen counters with a Giani marble countertop kit. The only problem is that I can’t remove the backsplash and part of the laminate is coming off. I tried ironing it back together but it’s not working. I’m afraid to use contact cement - it’s fatal if ingested and has high VOCs, I’ve read. Do you think a product like Simple Mat would work? Are there any other adhesives that would work? I tried Gorilla Glue with no luck. I’ve already added the marble look to half of my kitchen.

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