How do I get my iTunes "Album Artwork" to add to the individual files instead of "~/Music/iTunes/Album Artwork/" iTunes saves Album Artwork to ~/Music/iTunes/Album/Artwork/Cache/[some seemingly random folder name here]/
The problem is that if I move actual MP3 and AAC files from this computer (and/or iTunes database) to another one, I (assume that I) will lose the connection between those songs and the cached artwork.
Right now there is 826 MB worth of of cached images in 950+ files.
I am almost certain that it is possible to add album art directly to the media files, but I need a solution which can be automated (at least most of it) because I really don't want to do this 950+ times, and I have a lot more music to clean up in the future.

Footnotes:

[Non-free solutions are entirely welcome, but please let me know if your proposed solution isn't free, and how much it costs, if you know.]

I have both MP3 and AAC files, so hopefully any solution will work on either kind of files.
Check out this AppleScript from the excellent dougscripts.com: Re-Embed Artwork v.1.0. If that doesn't do it for you, you may find something else useful on that site. 

Note: I haven't run this script myself and can't vouch for its efficacy, though I believe its source is well-regarded. Use at your own risk.