Not sure where you're getting your info, but the G4 shock is pretty bad. It's set up and sprung very light. And no, it won't fit on the G3. The reservoir is completely different and would interfere with the swingarm.
Get your rear shock resprung and revalved and you'll be good to go.
I started a thread yesterday on my G4 Shock Ohlins v re-valve it pretty much answers the question about your shock. My shock is max out on the heaviest settings for dampening and rebound and its still not good enough. I am just debating of going ohlins or re-valve.