Few things I do in this process. I don't know if you touched up on it, but the caps that hold the bearing race and spanner nut need to be marked so you don't mix them up, along with the bearing races.
Something people overlook when putting these together, is that these diffs need load on the bearings. To acheive this, I tighten the ring gear into the pinion until there is no backlash at all, then give that spanner about another 1/4 turn. With no backlash, tighten the pinion side spanner until you get .004" - .006" (suzuki spec is .008, but they tend to last longer with slightly less) backlash, tighten your caps down and make sure you can turn the pinion. You gotta make sure you have consistent backlash throughout the rotation of the ring gear.