So unless I'm practicing for an airshow or there's a bandit on my six, a zoom climb gives me no real advantage over a normal Vy climb. Correct?
In theory, yes. Sadly, however, we did not record our location over the airport when we reached 1000' AGL using either method, which was a critical parameter to omit.
There is one possible point where a zoom climb MIGHT be "safer" than a "Vy climb -- and that's at its highest point. IF the zoom climb results in your ending up more directly over the airport environment upon reaching 1000' AGL, and the Vy climb does not, you should, in theory, have a better chance of making it back to the runway in the event of an engine failure at 1000' AGL by using a zoom climb.
Next time we will record our position over the airport when we reach 1000'. I suspect that the results will be very similar -- which should mean that there will be NO advantage of a zoom climb, other than the fun factor. But until I test it myself, I shan't say for certain.
Since you are always higher above the ground at any OTHER point during a Vy climb, this ultimately means that your chances of returning to the runway are better in the event of an engine failure. Since you've got 58 seconds at any other point in the climb, and only 2 seconds at the highest point, the safety tradeoff is not a good one.
So, at BEST, a zoom climb will only be "safer" at the highest point of the climb. During the REST of the climb, the Vy climb is always going to be "safer". In the end, the results will probably match what we all expect -- which is that a Vy climb will almost certainly always be safer.
The surprising part, to me, is that the TIME to climb between the two methods is virtually the same. (Just 2 seconds apart, in my test.) I did not expect that.