Yea, in a way I want a solid roof over the trellis. Mostly for sunlight filtering. I'm thinking of Sunbrella fabric in a drape from beam to beam. I would sew rings to the fabric that would hook on hooks on the underside of the beams. Wouldn't keep rain out but I have more sunny days than rainy days. Go figure! Looking at fabric tomorrow!
( I know some great guys who do great work should you want a recommendation, Alan. They've done three projects for me and I'm thrilled with their work). They do live about 20 minutes north of me, however, far from Chandler.)