On the street I wouldn't mess with the gear ratio. A 400hp 408 isn't going to be a revving machine and is going to make huge torque down low, but if you're not fighting for every tenth it's not worth the trouble.
It's not hard to change the differential, but it's easy to do it wrong. I'm not sure how many Eatons I've installed over the years, but I've never had one that didn't go back in just like the stock one came out. That doesn't mean you don't need to check your backlash before and after just to be sure, but I would be surprised if it's not good to go with the same shims that it has now. That said, if you don't already have a press you should probably pay someone to do it.
I've got a TruTrac in both of my trucks. In the Lightning it's vastly better than the stock diff. When I'd hit the gas at 40-50 mph with the stock diff you could feel the rear end wallowing around trying to decide which side was going to do the work. With the TruTrac it's just 2 black stripes straight as an arrow with zero drama. In my driver the difference wasn't nearly as night and day, but after changing the clutches in the stocker 3 or 4 times I could have nearly paid for the TruTrac and it's still a better unit that needs no maintenance.