I have made similar repairs and will suggest you roll the rubber carefully back away from the damaged area and then clean and cover the rubber before removing any of the damaged wood. If not, the saw dust from the wood work will stick to the adhesive still on the rubber and cause you quadruple the work.
I tried the PL adhesive on the first RV I worked on for re-attaching the plywood to the roof and walls and the fiberglass to the wood. It didn't cure quick.(after 3 days it was still not cured). I assume it is an air cured adhesive. Started over and experimented with different adhesives.
Moisture Cured Polyurethane worked best for me,(Gorilla glue). It expands and fills the cracks and crevices. You'll have to weight or clamp the wood in place to keep the adhesive from expanding and moving it.
If your damaged area is still wet it will take a bit to dry. I have had to lift the rubber and fiberglass away from the insulation for about a week before every thing seemed to be very dry.
The rubber is attached with either contact cement(older method)or a water based acrylic adhesive. For contact cement, you roll it on both surfaces a few feet at a time and let it dry before rolling the rubber out. The acrylic is rolled on to the wood and then the rubber rolled out on the roof while it is still wet.
Beaded Polystyrene does hold water, so make sure it is dry before closing the roof up. If you aren't sure, the expanded sheet insulation the home stores sell is a good replacement and isn't too expensive.
Good luck with the project.
Your welcome to PM me if you need more opinion.
