How can I get explicit versions of songs from iCloud?

I know this is not what you want to hear, but there is currently no workaround for this problem, and Apple has supposedly been working on this since February.

When you say

Just to clarify, I'm what has happened is that my iTunes match version of a song is the clean version. What was uploaded was not.

it makes it seem (from my understanding of the question) that you have a misconception of the iTunes Match service. iTunes Match identifies your songs (and the explicit ones) and ties them to your Apple ID so that every device on that Apple ID can have streaming and downloading rights to higher-quality DRM-free (256kbps) songs it matched it to, not the songs that you "uploaded".

Although, the fact that it probably isn't really fully uploaded may contribute to your problem. Apple's "uploading" process most likely fingerprints the song by taking a short sample of it rather than the full song. This means that it is difficult to tell whether the song is clean or explicit, and Apple has acknowledged this. Some users have even reported iTunes Match giving them the instrumental version of an album.

This is a bug in iTunes Match that will require a new method to match songs. Currently there are no workarounds, but you may phone Apple to fix the songs that you want explicit or complain on their feedback page.