There's a tool that will allow you to decrypt your iTunes .m4p files (m4p is basically DRM'd m4a), the only caveat being that your iTunes account ID will remain "branded" to the file. The reason for this is that the author is not advocating piracy; he's advocating for true "Fair Use", which would allow you to convert your iTunes songs to any format you like, and by extension, listen to the songs on any platform or device. So, your account ID stays with the file, and thus any attempt to disseminate the file across the Internet could, in theory, lead "authorities" back to the original owner.
Anyway, the tool is called HYMN (Hear Your Music Now), and can be downloaded here:
http://hymn-project.org/
HYMN also has a sister project called jhymn, which provides a simple GUI, but jhymn requires the Java Runtime Environment and some know-how to use. There are plenty of discussions on the Web that detail how various users have been able to get HYMN to work in Linux. Those new to digital audio and Linux may want to avoid this option (but it will never hurt to try). Naturally, Apple plays cat and mouse with HYMN, so newer songs purchased from the iTunes store attempt to defeat the decryption capabilities of HYMN. Thus, in my experience, not all songs can be decrypted.
That being said, I know that you already did the conversion, but what you basically did was convert all of your audio from a decent-quality digital format to a low-quality analog format (inside a huge WAV file), and then back to an even lower quality digital format. If you don't really care, then I'd just stick with what you've already done. But I'm posting this information for the benefit of others who may have the same question.
Another alternative would be to do what Simon Bridge suggested and burn your iTunes songs to CDs. It'll take you forever and you'll have to waste a bunch of CDs, but you'll be able to maintain all of the original data from the m4p file. You could then rip the CDs to a lossless format, like FLAC (Free Lossless Audio Codec), which has no proprietary restrictions, unlike most other such formats. You would end-up with a FLAC file that is much larger than the original m4a file, which will be the case with any iTunes file (since the quality of iTunes songs is mediocre and the files are fairly compressed).
As another poster mentioned, you probably realize now what a sham iTunes is. Buy your music from a company that doesn't employ ridiculous DRM measures that obstruct paying users from exercising true fair use.
Good luck!
How to play m4a on Rhythmbox
