Excessive play in steering wheel

LOL, well, we have focused on the steering boxes, partly out of general conversation. Rereading you original post, I thought you side 1/8" play but you said 1/8 TURN at the wheel; that is HUGE and explains having to steer like a maniac all over the place! That comment makes it pretty certain that you have a number of badly worn steering and suspensions components, as mentioned before. I would not be driving that car, and certainly not with a new 360 in it!

Steering: Steering shaft coupler, steering box, pitman arm, idler arm, tie rod ends.
Suspension: Control arm bushings, ball joints, strut rod bushings.

Sounds like time to jack up the car on stands, and go through the steering parts and find the loose item(s) and replace. And the same for the suspension parts, although those are harder to test; look for bits of rubber hanging out of the bushings, cracked and rotted rubber at the joints, and so forth.

If 'twer me, and the car's maintenance history was unknown, and I found a couple of bad parts, I would just shotgun the whole steering and front suspension with new parts, with the possible excpetion of the box: I would price that out and if too pricey, then test and adjust on that to see if it would come close to spec. And with 1/8 turn of looseness at the wheel, I would expect all sorts of worn/bad parts. Just 20-30 year old dried up grease in the joints in a car that has been sitting will cause problems. The parts don't cost THAT much and an all new setup will be a dream to drive.

It is not a job for a pure amateur, but if you are decent with tools and cars and have some room to work, this is something that you can do at your home shop. And unless I knew a shop that really knows older cars well, I would do it myself for the quality control. It does require some special tools, and a vice and a few big sockets, a lot of rust penetrant, and some occasional swear words, and air tools make it a lot easier too. You might want to take a few things to a shop with a press.

And BTW, a power steering box will have some play when the engine is off that a manual box will not have. This due to the valves inside the power box that are directly actuated by your steering input.