I've used the following to very successfully repair split grips and forearms...
1. Use a dremel to hog out a channel on the backside of the grip. Undercut it a bit to provide a "key" lock. Go at least 1/2" farther that the extent of the crack on the outside of the grip.
2. Drill a small "relief" hole through the very end of the crack. This relieves the stress that is causing the crack.
Be sure to save the dust & wood fiber from these two operations, as you can fill the drill hole with a mixture of dust & white glue to cut down on the appearance issues.
3. Clean thoroughly to remove all dust.
4. Using epoxy glue, accraglass, or a similar compound, fill the channel that you just cut into the grip. Be sure to spread the cracked area slightly so that you get the cracked edges to bond, as well. Don't let it drip through the crack, though, as it can take the finish off the grip pannel.
Smooth the bonding compound to match the contour of the back of the grip pannel so you don't have to do a lot of sanding.
5. Clamp, and let to dry.
I've fixed probably a dozen or more items using this method, and I've not had the cracks reappear.