protected aac audio file/.m4p

I have about 180 protected AAC audio files in my iTunes library. I have read the instructions that if I remove these songs from my library and download them again through the store they should be swapped for Purchased AAC files that I am then able to convert to .mp3. I've gone through this process. In iTunes, the songs are now listed as "purchased AAC audio files" but I still can't convert them to .mp3 - the underlying source files are still in .m4p format instead of .m4a. I've verified that the .m4p files are being removed and the iTunes store download is replacing them with the same file format.

What's the trick?