I used joint compound (yes, the stuff that goes on drywall). It filled the small gaps and screw holes nicely. Sanded smooth and reapplied. Sanded again and vacuumed. Kilz Premium over the entire surface. Let dry for 2-3 days, longer in high humidity. Measure out the centerline and snap a chalk line. Set tiles according to directions.
Relax and enjoy. Sleeps up to six and two dogs.