CFW = Custom Firmware, basically I modified firmware not supported by Sony.
6.20 is an OFW (Official Firmware), which you can't hack with.
And it technically would work on a PSP 3000, if you were running custom firmware on it through Chick-Hen.
Although I don't think you can use that since you've updated (or got your PSP with) 6.20.
You'd have to wait until a 6.20 Chick-Hen were available, or until the PSP 3000 is fully cracked (if ever).