The best way to do it would be to get a magnetic dial indicator (they're not too expensive from harbor freight). Stick it on the housing and adjust the dial so it touches the outer edge of the ring gear tooth. Hold the pinion and rock the ring gear back and forth by hand to measure the backlash. Once you remove the carrier and replace the spiders, install a locker or whatever then just set the dial indicator back up as close to the same as before and remeasure. Adjust the ring gear until you have the same amount of backlash as before then tighten both rings some to set the carrier bearing preload. Double check the backlash and readjust if needed.
If the backlash is the same after as it was before then nothing should have changed.
