"The funny thing was that there seemed to be a lot of play when the wheels were relatively straight but once the wheels were turned a bit there wasn't very much play at all."
If you were testing sitting still with the engine off, this is a sign that the sector gear is worn beyond useful adjustment. With a new box, you would expect less play at the center.
If you were testing on the road, while turning, the steering will be loaded in a turn. This will take out all impression of freeplay, unless a tire hits a road imperfection.
If testing with engine off, more freeplay off center while still a bit at center - you can often adjust it out, or at least minimize it.
'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7