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Try the kit and get a puller if you want to. BUT..If it's leaking now, theres a decent chance that the shaft has a flat spot from wear. Check that out the best you can when you tear it down. If it is worn, take back the kit and get a new or junkyard box.
My truck leaks in the same spot as your bros except I can keep it from leaking if I park the truck with the wheels strait....