I was able to work on my problem a bit today. I pulled the axle out and shined a flashlight down the tube and saw what appeared to be a thrust button. I tried fishing it out, but it just dropped down inside the differential housing.

I adjusted the end play as much as possible, but still ended up with 1/4". Because of this, and like someone mentioned, I'm wondering if the bearings aren't pressed on all the way. I measured 25.25" from the end of the spline to the start of the bearings. I'm not sure if there is a spec for this.

I was able to find a spec for the axle shaft length (end of spline to outside flange) of 29 3/16", and this measured fine on mine.

Thanks a lot for the help and bearing with me!