To hold my tripod chair, I used a couple of 4" corrugated drain fittings (a coupling and a gutter adapter). These are extremely light and add very little weight. I do intend on putting a piece of the 4" corruaged drain pipe to connect the fittings. Just haven't found a scrap piece yet. While the chair won't fall out, I do have a velcro cable wrap to secure it against the handle if I know I won't be needing it for a while.
For a rain setup, I found an old pole from a badmittion set that I hadn't gotten around to tossing. I attached this to the shaft with what is essentially a very large saftey pin. My umbrella had long since lost it's handle and simply slides into this pipe. When not in use, I use a couple of velcro cable wraps to hold the umbrella and attach the extra pole to the bottom of the box.