Logo conversion from jpg to Adobe Illustrator

I need a bipmap logo converted into a vector based one (Adobe Illustrator). The vector version should have only 4 colors and need to be as accurate to the original in colors and mood as possible. It would be great if the logo worked on both white and black backgrounds (so 4 colors in the logo, background color separately). Attached are a small image of the logo and of a one colored vector version, both available in full resolution to the provider taking the job. The word LIVE is nicely in vector format already. Focus mostly on the Kung-Fu- part. Also attached a quick test I did on letter K of the logo. The conversion could be something like this, but even smarter if you have a better idea for it. If possible it would be great if there was a way to maintain the grittyness in the look of the original one. E.g. making the edges rough, not fully straight divisions between the colors? I need to have all rights to the created vector form. I'm a hurry with this one.