Ok, I checked it out. I still think that shims and pins are in correctly. However, I did that not too many miles ago and then noticed the play after. Who knows how long something was wrong before that. One pin was cracked back then too.
With the shaft off, I have .015 play in/out on the output shaft. I guess that's it.
Now, how hard is this to fix? Can it be done by a DIYer?