Working to each material's strengths ~ and with clamps not so tight as to squeeze out all the adhesive ~ I've driven self-tappers through each stripwood beside the foam laminate too.
Don't drill all the way through both spars, as you'll want the fasteners to take best hold of each side. I've also used over-long screws because (a) I've a box of them and (b) the ends can be taken off with an angle-grinder, making me look like a real man in the eyes of Shania Twain.
