I don't think that tool can be used to measure backlash, but i might be wrong on that. My friend has a similar tool you posted a pic of, that we use to measure the pinion depth, and then we use a dial indicator with a magnetic base for the backlash readings.... One thing we do when setting the pinion depth is to pick up an extra bearing and then take a die grinder and take just enough the inside so it easily slides on and off the pinion...that way you don't have to continually press on and off the bearing while doing your iterations to get the right pinion depth. When you get it set, you then press on the good bearing....
Another tid bit, if you are putting in new gears and such, you'll probably find that getting the torque values on the ring gear bolts while holding the carrier is rather difficult, so you take your wheel, plop it on the ground, put the axle in the rim, and then slide your carrier over the splins on the axle. You will then be able to hold that assembly enough to torque down the bolts...
Nate