How to play previously DRM protected content in 3rd party iOS apps?

I have a collection of tracks which I purchased from iTunes around 2008, which have the iTunes DRM protection. I would like to play these tracks through 3rd party iOS applications. Specifically, the applications "NuVo Player", "Sonos", and "Ambify", although this seems to apply to all 3rd party music apps.

To remove the DRM from the files, I signed up for iTunes match. I enabled the service in iTunes, and let it scan my library. Once it was complete, I deleted the tracks which have DRM, and used the iTunes match service to re-download them. I used the Finder to inspect the new files, and verified that they are no longer protected. They are .m4a format, and are capable of being played by 3rd party applications in OS X.

I then removed the protected files from my phone, and manually re-synced the new files to my phone. Even after doing this, they are unplayable by 3rd party iOS apps. Unsurprisingly, syncing this .m4a file to a new device (which never had the protected version) allows it to play.

It seems that metadata of some kind may be retained on the iOS device. I suspect a full device restore would fix the problem, but I'm looking for a less intrusive solution.