Hey!
You could use a walking stick as a prop, and have other props on the stage like a walker, or a coffee table on wheels with a radio or a lamp on it.
With your character sitting down - you could (and I'm getting creative here), hold the straight end of the walking stick, then reach with the walking stick and "hook" things with the curved end and pull stuff towards you. You could then even integrate other stagecraft into your monologue (i.e., if the lady reaches for a radio, or a torch or some shit, you can utilise sound/lighting as well as the obvious ones inherent in your monologue like costume/prop/acting).
That's one way to utilise more of the stage - i.e., to have furniture and other stuff (obviously you have to carry it into the monologue room, I forget the rules). Because your props can take up some of the stage, and then you can take actions like reaching for things without even leaving your seat.