Been there, done that. Though I will say with driveline slop the difference between say... 3.40 and 3.55 can, at times, be hard to discern. The 8" "should have a tag showing the ratio. When I would go to Pick A Part looking for an 8" rear I would always write in the dust on the rear glass the ratio - helps out the next guy from having to crawl under.
Once I tried to detect the 1st gear ratio of a Jeep Toploader. I had to crank over that V-8 engine by hand over three times before I could detect that it WASN'T the T-178 transmission I was hoping it was. I was more doing pull-ups under the Jeep than I was getting rotation.