I suspect the answer to your question will be "keep sanding"?
Why not take some superglue and glue the sandpaper to a block of wood? Much easier to hold onto and after you are done sanding this card the sandpaper will probably be done for anyway.
Pic 2: The tool, I don't know what it's called but, you scrape from one side to the other and it lifts plastic sheet off in layers and then once it gets through that, it takes the words off.