I still can't see where the problem is, need to be able to see it all together, and the location of the fork with all the slack taken out of it. A pic from below of the fork, and a pic of the z-bar should help.
I am not aware of any factory pivot balls that are adjustable, at least not GM ones, and no, it doesn't get adjusted. We are so far from determining if an adjustable pivot ball would be needed in this case, don't even think about that until everything else is eliminated.
Nails in the shifter? Are you still trying to install the trans with the shifter installed on it? If it's a Hurst shifter, buy a pit pack and the adjustment tool before you even think about installing it on the trans. Seriously. And you still need to ensure the trans is in neutral before you try to install the trans, so need to know which way the shifter tabs are pointing. Both forks should be centered, the slot/keyway should be vertical.
http://www.summitracing.com/parts/huu-3327302
As for watching the tines, or fingers, or whatever, compress as you tighten the bolts, yeah, it's supposed to do that, it's applying pressure to the disc so it engages. If it were completely relaxed, there would be no pressure applied to the disc/flywheel, and it would slip or actually, not engage at all. And it is important to go in increments around the pressure plate as you tighten the bolts as to not damage the spring material in the pressure plate. If it becomes distorted, it won't apply pressure evenly to the disc and it will fail early.
At this point, the only things that I can see that might be a problem here it either the throw out bearing is too short or the z-bar and/or associated linkage is installed wrong or are the wrong ones for the application.
The ball stud that goes in the z-bar on the frame side has a clip that retains it, has 2 nylon cup washers on either side of the ball, and a gauze washer. The threaded part of the ball is slotted/keywayed and goes into the slot in the plate. If the z-bar has a grease fitting it can be greased, if not, you pack it with grease.
A service manual would probably be very valuable for a number of items discussed here.
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1971 Trans Am 463, 315cfm E-head Sniper XFlow EFI, TKO600 extreme, 9", GW suspension, Baer brakes, pro tour car
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