69 Barracuda Clutch Shake Help Needed.

So you had it before, and you still have it after?
Are you running a pilot bushing or bearing? What is the condition of it? Condition of the fork pivot? Condition of the fork? Release bearing? Bearing retainer tube? Assuming acceptable start to rule out items with easy stuff.
I think I'd start by verifying both spring clips are correctly on the clutch release bearing. Secondly, determine whether the release bearing is in contact with all three cover fingers at the same time when pushed forward, by hand, using the outside of the clutch fork. Third, going around the fly wheel diameter, determine the disc and cover plate ring mismatch is the same all the way around.
Being "new" don't necessarily mean it's "good". Although unlikely, possibility is there for a disc that has a fat area or a cover that has weak springs or stretched eye bolt.
And don't overlook a bad u-joint in that easy check stuff.

I put a new pilot bushing in. Double checked the fork springs and throw out bearing along with pp finger contact. Based on my test yesterday, I think the clutch area is good.