Very nice looking cage and stand hosman! If you want to stabilize the rust on the bottom and are not worried about the antique aspect, there is a product you can buy. I have used it on rust on a trailer and then painted it black. It is Plasti-Kote brand Rust Converter. I bought mine at the hardware store. It chemically converts the rust to a black stable finish and you can then paint over it without bleed through. This is only if you are going to paint the base anyway. If you want to keep it as is, I would buy a brass brush at the harware store (welding section) to help get in the scrolls and scrub loose rust out.
As for a Hendryx cage bottom, I would just keep searching secondhand stores, SA, Goodwill, online auctions, antique shops, post a "wanted" on Craigslist, etc. as they made these cages for years and there are alot of them out there. The bottoms are the first to go because people did not clean them when they put them away and the natural chemicals ate away the metal.