Mine is different than yours; it is only 2 pieces, the top is attached to the center piece which then drops into the basin with the oil ( I have been unsuccessful in posting photos, I'll try again so you can see what I have). I read one thread where they seperated the top from the center part ( so it would look like yours) and did just like you with the paper filter sandwiched between the top and the bottom of the bowl. That would certainly be easy.
Lee.