Here's an option for a better fit. Still no drilling or permanent mount.
GPS cup holder mount
Or if you have access to a hole saw the same diameter of your cup holder you can drill a few wood discs and stack and glue or screw then together to fill your cup holder.
Both are very solid ways to mount something in a cup holder. And removable.
I mounted a very large chart plotter in a boat cup holder using the second method.