The manual Vettes get a "Computer aided gear selection" which locks out 2nd and 3rd gear under low throttle and slow speed shifts from 1st gear after the engine has warmed up.
When your shift from 1st hangs up, do you notice a "1-4" light on the dash?
If so, it is an indication that CAGS has been activated.
There are "eliminators" available from several sources that 'bypasses' the CAGS operation at the transmission and allows you to shift from first to any gear and any throttle and speed.
Check out this article:
Shift blocking - Wikipedia, the free encyclopedia