You don't need to take the diff cover off to determine the gear ratio. If you've already lifted the back of the car off the ground and both wheels turn together (because of the limited slip) just count how many driveshaft rotations it takes to make the wheels spin one full rotation. It can be hard to judge portions of a rotation on the driveshaft but if it's a 4.11 it will be pretty easy to tell because the next nearest ratios are a ways away (3.90 and 4.33(?)).

If you're down where gear ratios are bunched closer together (3.23 3.36 etc) you can get a more accurate read by spinning the tires 10 rotations then dividing the number of driveshaft rotations by 10. You don't even need to estimate the last partial driveshaft rotation because you'll have the first two digits of your ratio just by counting complete driveshaft rotations. For example, 37 and a bit more driveshaft rotations can only be a 3.73.