Ranger, the most important thing you can do, other than checking in 4 places around the ring, is to rotate the gears back and forth as far as you can, grasping the ring gear, and feel for any "roughness" in the gear mesh. It should feel quite smooth, no light "scraping" sound, or feel. For best results, grasp the pinion flange while doing this, to increase pressure on the teeth.
If any scraping feel is present, those gears will make noise in service, just as sure as hell is hot. The pattern you show here is acceptable according to Ford Shop Manual, and I would be willing to go with it, IF, big IF: diff bearing preload is adequate, and pinion bearing preload is adequate. I always lean towards a bit MORE lash, rather than less. Racers know this, whose axles get super-hot. Pinion length increases, and lash becomes less the hotter the gears get. With what you have, the "feel" is very important.
Let us know, please. imp
Don't cut your fingers on the ring gear, use a rag!