I went from much worse than yours to this:
I first soaked the grip in lacquer thinner for a week. I then brought a pan of water to boil (outdoors!), and carefully placed the soaked grip into the water. The boiling water caused the lacquer thinner to be rapidly expelled from the grip, taking with it grease, grime and dirt. I do mean rapidly, you need the pan to be only half full of water because this causes a foaming that can quickly overflow the pan.
I repeated this process three times, then let the grip dry for two weeks. What you see above is the result.
ETA, I have no reason to think that gasoline would work any different. Easier to come by, maybe not as expensive. Be careful in either case, you don't want a fire!