The H.D.I. doesn't measure rocker (by which I assume you mean the blade curvature along the longitudinal axis from toe to heel) at all.
Edge Specialties, that sells the H.D.I. says
on their websiteTroubleshoot:
Check for accurate hollow depth
Check for edge balance
Check rocker radius
The H.D.I. is the only measuring tool that indicates the precise depth of hollow, the edge balance and rocker radius. This indication by the H.D.I. will totally remove the skate grinding guesswork and deliver confidence to the skate sharpening professional and skater.
Perhaps they mean ROH (radius of hollow) rather than rocker? But elsewhere on their site they use "hollow" and rocker the same way we do.
I couldn't figure out from the pictures how the HDI would measure rocker - I think you need at least three depth measurements along the length of the blade to do that. Did they make a mistake in their ad?
(Such a mistake would actually be consistent with the fact that the same page lists a table with the correspondence between hollow depth and ROH - though such a table can only be accurate if the blades are still sharp, but have been very lightly deburred, so there is no foil edge sticking above the hollow/side corner. On a dull blade, they would be in accurate.)
Also, as near as I can measure it without extreme skill, using my calipers (which read to .0005", but I'm not that consistent), Berghman sharpeners need a flat blade region at a height above the edge of
.3820" = 9.690 mm
I can carefully make it work with my old style Matrix blades (though I'm not sure the coarse crumbly old stone - possibly a natural "grindstone" - would work on stainless steel blades) - but I'm not actually clamping on the runner, or even the tilted surface next to the runner. But it was certainly easier on parallel sided MK Dance blades, and flat sided Coronation Ace blades. Of course, since old style Matrix runners were removable, I could do it more easily by removing the runners from the chassis - but that is inconvenient for a quick sharpen at the rink, and I tried to avoid demounting the runner as much as I could with those stupid soft aluminum bolts and nuts. New style Matrix runners are not removable, so doing it that way simply isn't an option anymore.
Also, all Berghman sharpeners were designed for .5" ROH. I once tried wrapping tape around a 3/8" radius stone from my Pro-Filer, and putting it in the Berghman holder, but the tape compressed a bit inconsistently, and I didn't like the results. So I bought a used 1/2" (Hockey) Pro-Filer on the web and used its stone instead - which worked, on rental skates - I didn't want that .5" ROH on my "real" blades.
So - unless the Phoenix blades have a flat surface at that height to clamp on to, all the way down the length of the blade, Berghman sharpeners would probably not do a great job on Phoenix Blades.
Help me to figure out why they don't create nice flat surfaces to clamp on to, on Phoenix blades?
P.S. I'm not sure there has to be significantly more sound-emitting surface area on Chassis+runner style blades, but your idea that noise is partly scattered out of the steel by a boundary layer effect sounds plausible. Could one theoretically use a sound-absorbing material between the chassis and runner without adverse effect?