So you have 76mm to work with... but you lose some of that to the side panels and the mobo backplate, but even so I'd say that it'll fit. That's about 3 in. if you were wondering. I'd be worrying more about the torque that thing'll put on your board... I'm surprised that you don't need to mount the upper end on the case supports to keep it from tearing off. At any rate, good luck with the HS.
I have a wavemaster case and a Hyper 6 and it fits fine. The nice thing about it is that with the wavemaster case the rear exhaust fan lines up pretty well with the Hyper 6. As far as mounting the thing it comes with a steel backing bracket for the mobo so its pretty sturdy. Just don't be banging the case around, lol.
BrandonV, how did that Zalman fit with your Abit IC7 Max3? Did it interfere with the northbridge cooler? I was wondering it the Hyper 6 would fit on that mobo without hitting the NB HS.