Any suggestions on how to finish 3/4 inch x 3 1/4 inch solid oak adjacent to a 9 foot long sliding patio door? I don't see how to attach any quarter round or any other trim to the bottom face of the patio door frame to cover the expansion gap for the flooring. The room is 30 feet wide so leaving room for expansion along the door seems necessary.

Use an endcap molding.

Sometimes called a square edge or, carpet reducer or, baby threshold.

I will have my moldings before I start near the doorway, so I can judge my expansion by the molding I have in my hands, dimensions. That way I'm not cutting floor to accomidate the leg width, or molding profile.