I have seen new clutch discs with a bit too much fuzz on them cause this.
I hesitate to mention this becasue your newer type clutch is a little different than the older firstgen stuff I'm familliar with.
But, consider that the new disc has a wavy plate in it's middle called a "Marcel" and the new material may have a rough surface that is combining to require more travel to the throwout bearing than you have.
We managed to almost eliminate the freeplay of the 69 Z/28 we had trouble with and put the car in gear and started it with the clutch pressed down.
There was drag but it worked and allowed driving around town slowly and doing some starts with "extra" clutch slipping to wear off the fuzz on the disc.
If this works on your car, be very careful to allow time after a start to allow the clutch to cool off before slipping it again.
After a couple of half hour trips around the neighborhood we could put it in gear from a stop.
Be very careful if you try this as if this isn't the problem the car will not stop when you start it in gear.
I don't know if your year has an interlock to prevent starting this way...
You may consider drilling a half inch diameter hole just below the clutch disc to enable viewing the disc and see if it's disengaging at all.
If the disc was put in with the springs toward the engine you would have this problem too.
Make sure everything else is correct before trying this.
Check my web page for First Gen Camaro suspension info:
David's Motorsports page
First Gen Suspension Page
67 RS 327
69 Camaro Vintage Racer
65 Lola T-70 Can Am Vintage Racer