Keith, I suppose you are talking about duplex mats. A lot of framers here use precovered beveled boards so applying the paper to the bevel isn't an issue. There are a couple of trade names, but they escape me at the moment.
If you are looking just for the adhesive, not the paper, you might want to give acrylic gel medium a try. It can be applied to the back of the paper, and to the bevel and adjacent sides of the foamboard. If it doesn't stick like a contact adhesive, heating it slightly with a tacking iron will reactivate the medium.
What you call woodpulp is known in the US by it's trade name Upsonite. I personally stay clear of the stuff because of its high, um, wood pulp (potential acidity) content. A better choice would be 8-ply rag board.