DSF

Have you tried using a layer of ironing board felt on top of the platern.....yes yes i know its my answer to a lot but it works

The base plate has a nice thick mat and I placed a silicon baking mat on top. I have no more boards left now to try anything else. This may be an expensive gift.

ok i know you will have a nice thick probably rubber mat on the platern BUT i used to have problems with pressing things like placemats quite similar to what you have displayed, i found that by putting a layer of ironing board felt ontop of the rubber mat this got rid of the problem . my theory is the heated plate probably isnt truly flat by putting the layer of felt ontop of the platern when you press a flat object ie placemat then this sinks slightlyinto the felt so if there is somewhere thats uneven this should get rid of the problem

Is your press a clam or a swing press? I have found that some clam presses give uneven pressure across the platen whereas a swing press gives more even pressure across the platen.