I am in accord with eightbore and others---I don't believe a high-stocked heavy trap gun is the way to go on ZZ birds (Helice). I personally shoot either a 30" barreled S x S or what might be considered a classic light pigeon gun O/U, but in each case stocked somewhat between field and trap dimensions. This is my definition of what someone else described as "lively", a gun that can be moved relatively quickly to a fast changing target. Not at all sure how these compare to Rocketman's various numbers, but Don, we'll have to do some spinning on the MOI machine.
I agree with an earlier poster that only some of the birds are rising, the rest are at all kinds of heights/angles etc. With a high POI gun, what you gain on the rising birds you more than lose on the others. But of course, I'm not a very good shooter at Helice, so I could ask myself--what do I know! Keith