The problem with trying to attach anything to a liner is that it is smooth (glossy) and it will be hard to get any kind of adhesive
to stick to it. You have two choices, you could grind the surface to make it rough and there by providing "tooth" for the adhesive
, or you can mechanically fasten with screws. A potential problem with screws is that they might protrude on the backside and may be a problem depending upon where you're applying it. Also with screws you're are either going to be looking at a lot of screws or you could set the screws deeper and plug
the holes and the wood would need to be thick enough to accommodate them. With the gluing method, you would have to apply pressure to the strips until the glue sets up and the best glue would probably be thickened epoxy
. Another possibility would be to use solvent based construction adhesive. You might be able to get away without grinding the surface with this stuff, it's very tenacious. If you could find an inconspicuous place and test it. One advantage with the const. adhesive is it could be removed with lacquer thinner without harming the fiberglass
although it would be a chore.
With either the screwing or the grinding first methods there is no going back.
One other method would be to lay up the pieces in a panel first maybe on 1/4" plywood
and the attach the whole thing at once possibly screwing around the edges . This of course would have to be relatively flat surface.