Strange Clutch Issue

Assuming that;
you installed the disc with the flywheel side to the flywheel
and the BH is correct for the input retainer, and
the over-center spring is installed on the Pedal assy and
the downrod does not rub on the firewall, at full travel
Then
Make sure your Zbar is anchored on the frame end by that horseshoe wire clip. The clip goes into holes in the Z-bar and thru to a groove on the od of those white plastic ball receivers.
The installed Z-bar should be parallel to the ground in rear view; and at about 90* to the centerline of the car, as viewed from the top.
If you have headers, make sure they don't rub on the clutch business, even when torqued over by the Power of the running engine. Your engine probably needs to be tied down.
After the freeplay is set, the fork should be near to touching the forward edge of the Bellhouse with just enough room to install the boot AND near to the center of the window, vertically speaking.
If it is not, you got wrong parts.
The adjusting pushrod should be running straight back towards the rear-end about parallel to the centerline of the car, and parallel to the ground. If it is not, you got wrong parts.
A mentioned above, check you engine mounts; all three of them.
If an engine mount is broken, you should feel the shifter torquing over with power application.
To check the engine mounts you sorta need a helper.
Set the park brake, Put the trans in gear, slip the clutch, while the helper observes the mount. If the mount cannot be seen just watch the carb jump up and down.
Reverse is checked the same way.
For the trans mount;
The old style pre 72, you gotta lever the trans up off the mount.
For the new style, it has a thru-bolt and cannot break .... but it can wear out. If the bolt is not in the center of the spool, it should be replaced, but it is captured so it will not likely make trouble.

Ok so happy hunting