John, the solution to your problem is to build up the substrate to a thickness which will accept fixings, but to do this you need to use a 18g or 23 g brad nailer (air or electric) plus a PVA adhesive and fix additional strips onto the existing board. This thickness will then eventually hold screws.

I did exactly this job on a RV in Florida back in 2001.

Didn't have to go looking for studs in Florida back then ...