na! i wouldnt bother with any of the actual main earths as i doubt it will be any of those, it might be though. especially if its been faulty before.
if your not getting any other problems, such as lights dimming or starting/charging problems then i would concentrate on the stereo earth itself first, if wiring it to the car body sorts it, then the gearbox earth is definately not causing you any problems.
the one to look at is the black wire coming out of the back of the stereo loom, it will probably need cutting and replacing with a wire attached securely, direct to clean metal car body, so the handbreak or other bolt/screw in the passenger compartment would be a good place to start.
however, if the gearbox earth is faulty then replacing the one from the stereo will not solve much because all you will be doing is making a good stereo earth wired up to a poor connection to the battery ( through the car body)
are you running an amp? if so the ones to really watch are RCA cables next to power cables as they can interfere with each other because of the small currents carried by RCA's but i ive never noticed it when they are running together, although I run them seperate because its just something ive heared too, bit of an urban myth I (and many others!) reckon. This also definately wont effect any speakers running off the HU so its easy to find out if this is causing you problems ( which i very much doubt it is!)
ground loops are quiet common though, get a ground loop isolater from halfrauds to solve that problem.
if its an alternator whine, may need an alternator surpressor for that, again im pretty sure halfords sell them. the stereo earth will be the way to go first though.
