I've only thrown Z. I think the concept that Predators and Firebirds are similar discs is erroneous, though widespread. Both are similarly overstable (unless you're talking super flat Firebirds), so I'm kind of surprised about turning into a moderate headwind. To me, that probably means either 1) Big Z isn't as overstable as Z, or 2) the awkward grip might have been responsible for an awkward release or some OAT? At any rate, if you're looking for a Discraft "Firebird replacement," I'd agree that the Machete is worth a try, even though I've only felt them in stores and haven't thrown one yet.
I agree with you and with pretty much everyone else that Firebirds feel way better for forehands. The decreased glide tends to make them very consistent as well. The thing about Predators is that they have much better glide. Throwing good backhand shots makes me feel like I'm channeling my inner Nate Doss, but you're right that it requires more arm speed than most of us mere mortals have. The glide also makes Preds fly quite different for overhands. I don't know if you're a tomahawk or thumber guy, but my only ace is a tomahawk with a Predator. I think it's because of the glide that it tends to come down at a little more of an angle, so that there's a better chance of hitting chains instead of dropping straight onto the basket. Anyways, since you've got the disc, you might as well give it a try.
After all that, I might as well admit that the Predator only rarely makes it into the bag (e.g. I recently brought it along as part of a 5 disc travel bag), while my Firebird will be in there for the foreseeable future, for everything from skip shots to headwinds to overhands.