I removed the metal pump thrust washer and replaced it with the thinner black plastic washer in the kit. It definitely helped. With the pump bolts tight, the front and rear shafts turn free with a rag. There is still no discernable end play, but the transmission doesn't lock up. I think this means that I'm only .010 or so from spec.
My transmission has a bolt-on yoke, so there is no snap ring. I always install the "fwd and high drums and front planets, input shell, etc" as a unit with the tail housing bolted on to hold the output shaft in position by the large tail shaft bearing. I am positive all of the clutches are properly engaged. There is a gasket under the pump and it is the same thickness as the original. I have not changed any of the thrust washers to needle bearings. The needle bearing races are in the correct position.
I've thought about this and the only way this could happen is that one or more of the thrust washers I changed must be thicker than the original. All the washers that were in my transmission when I bought it were in perfect shape except for one. I pulled out the one that looked worn this morning and most of the copper metal was worn off, but it had not worn down much into the washer itself. The only thing I can do at this point is to pull the transmission back apart and check every washer. This is a hobby project, so I'm not too concerned about it. It's frustrating because I know I have the darn thing back together right.