Since Yamaha's own speakers have 6ohms rating and realisticaly go down to 3ohms under certain conditions, Yamaha receivers do have a genuine low impedance driving capability and you can see that by the size of the transformers used in their receivers.
The point about headroom is that to get realisticaly high headroom from your existing amp, the replacement amp has to produce twice the power and the Yamaha is not rated at twice the output of the SONY. For bass it is better to add a good high powered sub like the Yamaha YST-SW1500 or a Velodyne or Def Tech rather than tax the amp and muddy up your main speakers by feeding them excessive bass.