Strange the C7 Z didn't feel as it pulls harder than the Cat because stock for stock it is the faster car. Like BLKOUT mentioned the 2017 or even newer would be the way to go as they remedied the cooling issue in the 2017s and up. The M7 transmission seems to not have the cooling issues as opposed to the A8.
I'd like to get into a C7 Z06 one day but few of its flaws such as cooling issues, rear end twitchiness/ unpredictably when pushing hard in the corners, oem wheels cracking and or bending, their A8 transmission shudders as well as not being that responsive, has made me a little hesitant.
Where the Z06 seems to fall short with the flaws I mentioned, the ZL1 seems to have none of those issues. This is definitely not to deter you away from the Z06 as I'm sure those flaws can be remedied with some sort of aftermarket support.
I admire those beautiful Z06s and still may look into one but at the same time the ZL1s are great too and maybe less issues to deal with, so something to consider. I'm a performance guy at heart and usually always like to upgrade to the faster car which is going to be the Z06 even though the ZL1 maybe the better engineered car.
OP give another Z06 a shot, maybe that one had issues.