Rick, I had a very similar experience with my '78 450 SEL. The problem turned out to be the steering shaft coupling, which is a universal arrangement as I recall. It is located just inside the engine compartment on that side of the firewall and you should be able to see it easily. The coupling connects the steering wheel shaft to the steering gear box via another shaft, which is the purpose of the coupling. There were two sets of nylon, or some sort of polymer, bushings which had worn out, cracked, and fallen apart around two of the four bolts of the coupling.
The slop in my case was caused by the loss of integrity of the coupling without the bushings in place. I could turn the steering wheel several inches (2 to 3 or so) just sitting in the car without the engine running. At highway speeds, I would actually get a chatter out of this coupling since the metal of the coupling plates were was hitting the bolts.
I suggest you look at this coupling before you spend a lot of time trying to adjust the play via a steering gear setting.
My alignment was good before and after this occurred, which really became severe on a trip of course.
The replacement of the coupling is not very difficult, but I had to remove the steering wheel, loosen the shaft at the coupling and pull it inside the steering column to enable the coupling to be removed and replaced. The manuals do a reasonable job of describing this process, but be careful on shaft alignment since you will loose the relationship of the two shafts once the coupling is removed. If this turns out to be your problem, I would recommend marking the steering shaft and lower shaft in some fashion (chalk? or tape?) before you separate the two.
Anyway, I hope this is your problem since it is a pretty inexpensive problem to fix. It is also a little dangerous since the only thing connecting the steering of the car to the power steering box is the four Allan headed hex bolts without the bushings in place to keep them from wearing.
Good luck.

Redflash

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1997 S600 Coupe
2002 Lexus SC430
2004 Lexus RX330 (wife's car)
Owned:
1993 500 SEL
1994 E320 (wife's car)
1987 300 SDL
1978 450 SEL
1980 300 TD (wife's car)
1969 280 SL