I have used a bamboo flooring on the ceiling of an accessory building and the higher heat at that level caused the adhesives to soften and start to move out of the bamboo.
Don’t know if this would happen with an engineered wood product, but I would stick to solid wood.
Also, drywall and paint first to stop moisture from moving into the ceiling trusses. The Stack Effect is a powerful force and any cracks or joints in the ceiling will allow water vapor into your attic insulation and trusses.
Q