I have a feeling you'll need much wider, shorter screws (with thread all the way up to the head) for the two screw holes on the top. Unless there's a centre block underneath the top at the back to screw into (rather than a smaller one just for the triangular tailpiece and strap pin), you've only got the thickness of the ply for the screw to get a purchase. Certainly the long screw supplied looks more like it should be holding the rear of the Bigsby tailpiece on, along with the strap button (though I may be wrong).
I'm sure other people have drilled pilot holes for the screws on the top, then put string through and pulled that out an f-hole. Then they've made some small wooden blocks with holes in the middle, pushed the string through and knotted it, then stuck epoxy glue on the top of the block, pulled it back inside the body with the string and tied a weight to the string to keep it under tension and hold the block against the underside of the top until the epoxy sets. Once dry, remove the string, extend the pilot hole through the block and then you've got a lot more for a screw to get a grip on and not pull out.