I wouldn't even think of trying to take a CV down with nothing but zeroes.
I would mention I am a bit scared with just staying low, although with high cover it wouldn't be as bad. The reason is I found the Hellcats incredibly dominating in the vertical fight. So a smart Hellcat looping through a bunch of Zeroes without high cover would be bad.
I recently retested the planes in this series with my test scripts (
http://www.errthum.com/warbirds/flight) and the Zero was neutered at some point since 2007. As mentioned here, the Hellcat can out climb the Zero and remain faster while doing it. My tests showed that the Zero had a higher ceiling, but found out that could be false security. I fought Todzla on the very edge of the ceiling (33-35k) and I could not shake him as he would do these vertical loops and dive and hop maneuvers that I could not maneuver quick enough around. I was losing angles to him with every series but luckily my wingman Timos came to my rescue and shot him down (with 40% of his ammo) when he made a mistake and stalled while putting some bullets into me.
Anyway, rambling, but I think forgetting the scouting, staying inside the ring, and stacking in layers are all good ideas. Fight our fight, not theirs.