What gains are you really going to get ? The gain will be bugger all anyway its not going to beat the ls engine if its a road car you drive everyday leave it alone , easy to see Im a country bloke whos cars spend most of their time at 100k's. 3.7:1 lsd? If you go 3.89:1 how many revs are will that be at @100k's
How much faster do you want to accelerate? Also keep in mind that with shorter diff gears (greater mechanical advantage) you will wheel spin easier so a diff centre upgrade will also be recommended to make use of the increased acceleration. Also keep in mind that with shorter diff gears what you gain in acceleration you loose in top end so car use has to be factored into the equation.