The community always comes to the rescue! This is the case with the Verizon Samsung Galaxy S III too when the good folks at XDA Developers recently unlocked its boot loader — instead of waiting for that special Developer Edition to land and empty your wallets.
However, if you have the phone and find the procedure cumbersome, there’s and easier one and it is available for free in the Google Play Store, given that you at least have rooted your device. The description also seems to include a very easy step-by-step guide: “open the app, press unlock, and you’re done”. Once unlocked you can play with custom ROMs like CyanogenMod, as long as you understand the risks involved with such deep level tweaking. The app is expected to receive an update soon to “revert back to a locked bootloader”.