4 speed problem

I have a 1969 GTS 383 4 spd with a problem. Shifting from neutral into 1st I have a severe shimmy/vibration. Once I am rolling it goes away. No problem from 2nd to 3rd to 4th. Any clues what could be going on. I have had the tranny rebuilt, new clutch, pressure plate, the bushing and bearing at the front as well as the rear tranny mount, thanks for any help or suggestions.
I recently went thru same thing on 69 GTS, I installed new z bar bushings and ball mounts,checked pedal bushings,pedal did not feel right,was a little hard to push and chattered and vibrated in first gear.the problem was clutch fork pivot mount in the bell housing,not sure what this piece is called,anyway it was cracked and flexing when I depressed clutch pedal. I was able to remove inspection cover and removed clutch fork out of bell housing,removed the two bolts that held the bracket on,inspected it and was cracked allowing clutch fork to move when pedal was depressed. I happened to have another bell housing I acquired and removed the pivot mount and reinstall in car. Works perfect now,I have not been able to find this piece anywhere. I could not see cracked in piece until I got it out of bellhousing