You don't mention the year of your Z either. If it's a '90 and has a tachometer error then yes you would be convinced that the Z has had a rear gear installed. Use a scanning tool and check the RPM's from the ALDL to confirm tach operation. All years could have the tach error but it's frequently found on the '90 and less frequently the '91.
I'm guessing that's your error situation!
Drive it with the scan tool attached and do the same or similar runs!
Check the rear axle ratio. It's discussed in this thread and I mentioned a couple different ways to calculate it and the latter using degrees or minutes of rotation was confirmed by the OP.
http://www.zr1.net/forum/showthread.php?t=21653