I don't recall seeing this characteristic of the HE-560 referred to as a "treble spike" (as in something that shows up on an FR graph) so much as I see people describing the HE-560 as a "bright" headphone at the upper end, which is a
little different. If there was a harsh high-frequency peak on the
HE-560 relative to the
Sundara or the
HE-500, I would expect it to be visible on objective measurements (see embedded links).
That being said, I have read anecdotal reports that the v2 and v3 have less harsh/bright treble than the v1 and v1.5, but as far as I'm aware there are no good, objective measurements of these new versions, yet. So no way to know for sure. I'm hoping someone posts measurements soon!