Here's a couple sugestions
Usually wantering all over the road is because they set the toe to a positive toe-out condition and may be due to a positive camber setting. My alignment shop did this to my 72 and it was rough to drive. They used the 68-69 specs. Some books have incorrect settings. Go to Vette Brakes and Products web site and print out the alignment specifications. They have 3 different settings. I would suggest picking the middle setting. Not the factory spec, not the full road race spec, but the one in the middle.
Post your alignment sheet read-outs. You shouhd have gotten a before and after read-out. This could tell us what may be wrong.
Also, if your steering wheel has play in it, it is a simple adjustment to tighten it up. Do a 1/2 turn at a time and test drive it between adjustments.
I have namual steering, so I have no real way to replace the steering bix grease on the factory box. I bought a grease fitting that replaces one of the bolts in the top of the steering box and some GM grease. I was able to pump the grease gun 200 times and still not have the box over full. I pulled a second bolt out to watch for grease. You don't wnat to fill it completely up, becasue it expands when it gets hot. I cycled the stering twice between each 50 pumps to help distribute the grese in the box. I am sure yours has power steering, so adding grease is not something you want or need to do.
For aligning the rear, the best thing to do is get adjustable strut rods. They are not htat expensive, and allow the shop to get your rear wheels very close to perfect. For the most part, the original shims in the trailing arms do not need to be changed.
Another thing is that maybe your idler arm has too much play in it. It is a simple replacmeent and can eliminate a lot of steering play. It gets the most wear of the entire steering system. new ball joints, tie rod ends, and control arm bushings will eliminate the rest of the play in the ssytem. I had a friend who owns a shop re-do my entire front end on my 82 for $650.00 which included ball joints, bushings, idler arm, tie rod ends, tie rods, and labor.