To set your backlash, you will need to move the carrier closer to or farther away from the pinion. I normally set it up by hand and then check it with the dial indicator and fine tune it from there. You will need to loosen one side and tighten the other side to move it where you want it. This is where the spanner wrench comes in. Make small adjustments and check after you tighten them.
The adjuster nuts are really helpful to move the ring gear back and forth. Unlike the 8.8 or Dana 44 that requires you place shims behind the bearing every time you need to make an adjustment, on the 9" you just loosen one side and tighten the opposite side to move the gear.
The new gear is so thick, that to set the backlash, I needed to remove some material from the pinion straddle bearing mount. It wasn't hitting, but it was really close. I pulled the carrier out and hit it with the right angle grinder so it would have some extra relief. I was concerned that things might "grow" when they got hot. It was basically casting flash and it was ground down before, but I feel better after I cleaned it up a little more. You can see in the pic that it has some room now.