You really want to use 1500 or 2000 grit sandpaper. You didn't mention this, but make sure you get wet/dry sandpaper, the dark grey stuff. If all you can find is 1000 grit, then here's an alternate solution. Cut the sheet into fourths and then take one of those pieces and cut it into half to create 2, one eighth, pieces. Take these 2 one eighth pieces and sand them against each other until they feel about as smooth as your finger tips.
