When we make foam panels stone walls we use a little rubber cement and the debris from texturing to cover the plastic washers we use to hold the foam to the frame. We normally have to glue these a couple of times to get it to blend in.
This time we tried using a circle of foam cut from 1" foam and then cut in half so it was 1/2" and glued it with gorilla glue to the plastic washer. We first sink the washer a little deeper so the foam disc can sink in. Then we texture it and heat gun it and it blends right in and much better looking than the rubber cement and debris technique.