the only time I hit the limiter on a consistent basis is in 2nd gear. I usually watch the tach like a hawk with my left eye in 1st as I find by not watching closely it is too easy to hit the limiter in 1st. If I shift by "ear & feel" of the motor in 2nd I will always hit the limiter, but then my only other vette was a C3 LT-1 car. So seeing 6 to 7 k rpms on a tach is "normal" for me! Even my DD, Cobalt Sport 2.4 DOHC/4V has a 6.5 k rpm limit on the tach!
JMHO, but 1st gear ratio is too big ( isn't it like a 2.63 gear? ) for the power available and the stock rear gear ratio. If I had money to waste I would like to see the Z's box with a 2.20 1st gear like the M22's used? That set up in my 72 LT-1, an M22 box with a 3.55 rear gear & 15" wheels, yielded 10 mph per 1k rpm in 1st gear. So 0 to 60 mph was done in 1st without even being close to the factory red line of 6800 rpms. To a road work person, having a "useable" 1st gear is a God send! Those pesky hairpin turns & all ya know.
Tom