Before all else, check all your steering components as Rick suggested. Tie rod ends, idler arm, upper and lower ball joints and control arm bushings can contribute to the sloppiness in the steering or wheel play when the car is moving. All components are easy check!

Steering box......
You should at least attempt to adjust the play in the steering box prior to doing a R and R.

The Adjustment Screw lowers the Sector Shaft into the housing and forces the Sector Shaft Teeth to mesh with the teeth on the Rack Block. This screw also sets the amount of end play of the Sector Shaft. This screw must have enough clearance to allow the Sector Shaft to turn without binding on the screw, but not so much that there is excessive end play in the Sector Shaft to affect gear mesh. The Adjustment Screw is located on the top and is set into place by a lock nut.

Honest enough answer for ya?